Electromagnetic Nondestructive Evaluation (XIV) - Volume 35 Studies in Applied Electromagnetics and Mechanics

ELECTROMAGNETIC NONDESTRUCTIVE EVALUATION (XIV)

Studies in Applied Electromagnetics and Mechanics Series Editors: K. Miya, A.J. Moses, Y. Uchikawa, A. Bossavit, R. Collins, T. Honma, G.A. Maugin, F.C. Moon, G. Rubinacci, H. Troger and S. A. Zhou

Volume 35 Previously published in this series: Vol. 34. Vol. 33. Vol. 32. Vol. 31. Vol. 30. Vol. 29. Vol. 28. Vol. 27. Vol. 26. Vol. 25. Vol. 24. Vol. 23. Vol. 22. Vol. 21. Vol. 20. Vol. 19.

S. Wiak and E. Napieralska Juszczak (Eds.), Computer Field Models of Electromagnetic Devices J. Knopp, M. Blodgett, B. Wincheski and N. Bowler (Eds.), Electromagnetic Nondestructive Evaluation (XIII) Y. K. Shin, H. B. Lee and S. J. Song (Eds.), Electromagnetic Nondestructive Evaluation (XII) A. Tamburrino, Y. Melikhov, Z. Chen and L. Udpa (Eds.), Electromagnetic Nondestructive Evaluation (XI) S. Wiak, A. Krawczyk and I. Dolezel (Eds.), Advanced Computer Techniques in Applied Electromagnetics A. Krawczyk, R. Kubacki, S. Wiak and C. Lemos Antunes (Eds.), Electromagnetic Field, Health and Environment Proceedings of EHE’07 S. Takahashi and H. Kikuchi (Eds.), Electromagnetic Nondestructive Evaluation (X) A. Krawczyk, S. Wiak and X.M. Lopez Fernandez (Eds.), Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering G. Dobmann (Ed.), Electromagnetic Nondestructive Evaluation (VII) L. Udpa and N. Bowler (Eds.), Electromagnetic Nondestructive Evaluation (IX) T. Sollier, D. Prémel and D. Lesselier (Eds.), Electromagnetic Nondestructive Evaluation (VIII) F. Kojima, T. Takagi, S.S. Udpa and J. Pávó (Eds.), Electromagnetic Nondestructive Evaluation (VI) A. Krawczyk and S. Wiak (Eds.), Electromagnetic Fields in Electrical Engineering J. Pávó, G. Vértesy, T. Takagi and S.S. Udpa (Eds.), Electromagnetic Nondestructive Evaluation (V) Z. Haznadar and Ž. Štih, Electromagnetic Fields, Waves and Numerical Methods J.S. Yang and G.A. Maugin (Eds.), Mechanics of Electromagnetic Materials and Structures

Volumes 1 6 were published by Elsevier Science under the series title “Elsevier Studies in Applied Electromagnetics in Materials”.

ISSN 1383 7281 (print) ISSN 1879 8322 (online)

Electromagnetic Nondestructive Evaluation (XIV)

Edited by

Tomasz Chady West Pomeranian University of Technology, Szczecin, Poland

Stanisław Gratkowski West Pomeranian University of Technology, Szczecin, Poland

Toshiyuki Takagi Tohoku University, Japan

and

Satish S. Udpa Michigan State University, USA

Amsterdam • Berlin • Tokyo • Washington, DC

© 2011 The authors and IOS Press. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior written permission from the publisher. ISBN 978 1 60750 749 9 (print) ISBN 978 1 60750 750 5 (online) Library of Congress Control Number: 2011928887 Publisher IOS Press BV Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 687 0019 e mail: [email protected] Distributor in the USA and Canada IOS Press, Inc. 4502 Rachael Manor Drive Fairfax, VA 22032 USA fax: +1 703 323 3668 e mail: [email protected]

LEGAL NOTICE The publisher is not responsible for the use which might be made of the following information. PRINTED IN THE NETHERLANDS

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved.

v

Preface This volume contains selected papers from the fifteenth International Workshop on Electromagnetic Nondestructive Evaluation, which was held in Szczecin, Poland, from June 13 to 16, 2010. Previous ENDE Workshops have been held in: London, United Kingdom (1995); Tokyo, Japan (1996); Reggio Calabria, Italy (1997); Chatou, France (1998); Des Moines, United States (1999); Budapest, Hungary (2000); Kobe, Japan (2001); Saarbrücken, Germany (2002); Paris, France (2003); East Lansing, United States (2004); Iwate, Japan (2006); Cardiff, United Kingdom (2007); Seoul, Korea (2008); Dayton, United States (2009). The aim of the workshop, organized by the West Pomeranian University of Technology, Szczecin, Poland and the Japanese Society of Maintenology, was to bring together scientists from universities and research institutions conducting in-depth research into the basics of electromagnetic non-destructive evaluation (ENDE) on the one hand, and engineers presenting practical problems and industrial applications on the other. Ninety nine participants from eleven European countries and from Algeria, Australia, Brazil, China, India, Japan, Korea, and the United States, were officially registered. Eighty papers were presented in all, among them five invited papers, namely: 1. 2. 3.

4. 5.

D.C. Jiles, Ł.P. Mierczak, Y. Melikhov, Detection of Surface Condition in Ground Steel Components Using Magnetic Barkhausen Measurements, S. Honda, Pipe Wall Thickness Inspection with Current Driven Thermal Method, J.S. Knopp, M. Blodgett, J. Calzada, E. Lindgren, C. Buynak, J. Aldrin, Computational Methods in ENDE: Revolutionary Capability for the Sustainment of Aerospace Systems in the 21st Century, Z. Chen, T. Hwang, L. Wang, S. Tian, N. Yusa, Investigation on the Features of the Electric Conductivity Around a Stress Corrosion Crack, S.C. Chan, R. Grimberg, J.A. Hejase, Z. Zeng, P. Lekeakatakunju, L. Udpa, S.S. Udpa, Development of a Nonlinear Eddy Current Technique for Estimating Case Hardening Depths.

Short versions of all the contributions have been published in the Book of Abstracts, and reviewed and accordingly revised full papers have been accepted and are now included in this volume: Electromagnetic Non-Destructive Evaluation (XIV) published by IOS Press in the series Studies in Applied Electromagnetics and Mechanics. In closing, we would like to thank the authors, session chairs, and reviewers for conscientiously executing their duties to maintain the high scientific quality of the papers published in this volume. We believe that the readership of this book will find the included papers interesting and inspiring. T. Chady, S. Gratkowski, T. Takagi, S.S. Udpa Co-Editors

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ENDE 2010 – Szczecin Poland Conference Organization The 15th International Workshop on Electromagnetic Nondestructive Evaluation, Szczecin, Poland, June 13–16, 2010. Organized by West Pomeranian University of Technology, Szczecin, Poland in Cooperation with Japan Society of Maintenology, Tokyo, Japan Co-Sponsors Japan Society of Maintenology, Tokyo, Japan Oddział Szczeciński Stowarzyszenia Elektryków Polskich, Szczecin, Poland Federacja Stowarzyszeń Naukowo-Technicznych NOT w Szczecinie, Poland ZAPOL grupa reklamowa, Szczecin, Poland Technika Obliczeniowa, Kraków, Poland Standing Committee F. Kojima I. Altpeter J. Bowler N. Bowler T. Chady Z. Chen D. Jiles J. Knopp D. Lesselier K. Miya G.Z. Ni J. Pavo G. Pichenot G. Rubinacci S.J. Song T. Takagi A. Tamburrino L. Udpa S.S. Udpa

Japan Germany USA USA Poland China UK USA France Japan China Hungary France Italy Korea Japan Italy USA USA

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List of Referees and Scientific Committee P. Baniukiewicz L. Janousek C. Bardel T. Jayakumar H. Brauer H. Kikuchi J.R. Bowler F. Kojima K. Capova D. Lesselier T. Chady P. Lekeaka-Takunju S.C. Chan N. Mahapatra Z. Chen A. Nishimizu W. Chlewicki D. Premel Y. Goto J. Pavo S. Gratkowski G. Psuj R. Grimberg J.M.A. Rebello D. He M. Shiwa H. Huang M. Smetana Organizing Committee Honorary Member: Rector ZUT Włodzimierz Kiernożycki Chairman: Tomasz Chady Co-Chairman: Stanisław Gratkowski Ryszard Sikora Stefan Domek Andrzej Brykalski Members: Piotr Baniukiewicz Wojciech Chlewicki Paweł Frankowski Justyna Jończyk Jacek Kowalczyk Krzysztof Kujawski Paweł Lesiecki Przemysław Łopato Lech Napierała Marzena Olszewska Grzegorz Psuj Tomasz Pietrusewicz Krzysztof Stawicki Barbara Szymanik Marcin Ziółkowski

K. Stawicki G. Steffes O. Stupakov T. Takagi A. Tamburrino T. Uchimoto L. Udpa S.S. Udpa G. Vertesy T. Yamamoto N. Yusa M. Ziółkowski

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ENDE 2010 – Szczecin Poland List of Participants Yuji Akiyama Kanagawa Institute of Technology, Yokohama 3-19-25 Shimosueyoshi, Tsurumu-ku 230-0012 Yokohama Japan [email protected]

Iris Altpeter Fraunhofer-Institut IZFP, Saarbrücken Campus E3.1 D-66123 Saarbrücken Germany [email protected]

Piotr Baniukiewicz Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

B.P.C. Rao NDE Division, Metallurgy and Materials Group, Indira Ghandi Centre Atomic Research 603102 Kalpakkam India [email protected]

Bilicz Sándor Budapest University of Technology and Economics Egry József út 18 1521 Budapest Hungary [email protected]

Hartmut Brauer Ilmenau Univeristy of Technology Helmholtzplatz 2, P.O.Box 100565 98684 Ilmenau Germany [email protected]

Andrzej Brykalski Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Stephen Burke DSTO 506 Lorimer St VIC 3207 Fishermans Bend Australia [email protected]

Flavio Calvano Università degli Studi di Napoli Federico II Via Claudio 21 80125 Naples Italy [email protected]

Juan Calzada Air Force Research Laboratory 2230 Tenth Street 45433 WPAFB USA [email protected]

x

Klára Čápová DEBE, Faculty of Electrical Engineering, University of Žilina Univerzitná 1 SK-01026 Žilina Slovak Republik [email protected]

Tomasz Chady Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Zhenmao Chen Key Laboratory for Strength and Vibration, School of Aerospace, Xi’an Jiaotong University 28 West Xianning Road 710049 Xi-an China [email protected]

Wojciech Chlewicki Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Georgios Christofi Department of Physics, University of Cyprus Building:ΘΕΕ 02,20537 1676 Nicosia Cyprus [email protected]

Thanh Long Cung SATIE – ENS Cachan 61 avenue du président Wilson 94230 Cachan France [email protected]

Rémi Douvenot L2S-DRE (CNRS-SUPELEC-UNIV.PARIS SUD) Joliot Curie 3 91192 Gif-sur-Yvette France [email protected]

Dagmar Faktorová University of Žilina Univerzitná 1 SK-01026 Žilina Slovak Republik [email protected]

Mouloud Feliachi IREENA CRTT, Bd de l’Université 44600 Saint Nazaire France [email protected]

Emna Amira Fnaiech CEA List Centre Saclay; Bât 611 PC120 91191 Gif-sur-Yvette France [email protected]

Bryan Foos First Principles Inc. 800 Harman Ave 45419-3432 Oakwood USA [email protected]

Paweł Frankowski Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

xi

Konstanty Marek Gawrylczyk Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Stanisław Gratkowski Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Raimond Grimberg National Institute of Research and Development for Technical Physics 47 D.Mangeron 700050 Iasi Romania [email protected]

Gyimóthy Szabolcs Budapest University of Technology and Economics Goldman Gy. tér 3 1111 Budapest Hungary [email protected]

Ammar Hamel A/Mira University, Bejaïa Route de Targa Ouzemour 06000 Bejaïa Algeria [email protected]

He Dongfeng National Institute for Materials Science Sengen 1-2-1 305-0047 Tsukuba Japan [email protected]

Tommy Henrisson L2S-DRE (CNRS-SUPELEC-UNIV.PARIS SUD) Joliot Curie 3 91192 Gif-sur-Yvette France [email protected]

Susanne Hillmann Fraunhofer IZFP, Dresden Maria-Reiche-Str. 2 01109 Dresden Germany [email protected]

Satoshi Honda Faculty of Science & Technology, Keio University Hiyoshi 3-14-1, Kohoku 223-8522 Yokohama Japan [email protected]

Huang Haiying University of Texas at Arlington 500 W. First Street, WH211 76019 Arlington USA [email protected]

Moayyed Hussain Benet Laboratoris Watervliet Arsel 12189 Watervliet USA [email protected]

Ladislav Janoušek DEBE, Faculty of Electrical Engineering, University of Žilina Univerzitná 1 SK-01026 Žilina Slovak Republik [email protected]

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David Jiles Cardiff University CF24 3AA Cardiff United Kingdom [email protected]

Hiroaki Kikuchi Iwate University 4-3-5 Ueda 020-8551 Morioka Japan [email protected]

Kim Jungmin Chosun University Seosukdong 375 501-759 Gwangju Korea [email protected]

Kiss Imre Budapest University of Technology and Economics Egry József út 18 1111 Budapest Hungary [email protected]

Jeremy Knopp AFRL/RXLP WPAFB, OH, 45433 [email protected]

Satoru Kobayashi Iwate University 4-3-5 Ueda 020-8551 Morioka Japan [email protected]

Fumio Kojima Kobe University Rokkodai 1-1, Nada 657-8501 Kobe Japan [email protected]

Eugeniusz Kornatowski Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Jacek Kowalczyk Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Marc Kreutzbruck BAM Federal Institute for Materials Research and Testing Unter den Eichen 87 12205 Berlin Germany [email protected]

Marc Lambert L2S-DRE (CNRS-SUPELEC-UNIV.PARIS SUD) Joliot Curie 3 91192 Gif-sur-Yvette France [email protected]

Brian Larson Iowa State University 175 ASC II 50011 Ames USA [email protected]

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Lee Jinyi Chosun University Seosukdong 375 501-759 Gwangju Korea [email protected]

Dominique Lesselier L2S-DRE (CNRS-SUPELEC-UNIV.PARIS SUD) Joliot Curie 3 91192 Gif-sur-Yvette France [email protected]

Przemysław Łopato Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Lim Tekoing CEA Saclay Centre Saclay; Bât 611 PC120 91191 Gif-sur-Yvette France [email protected]

Steve Mahaut CEA Saclay Centre Saclay; Bât 611 PC12D 91191 Gif-sur-Yvette France [email protected]

Kenzo Miya Professor-emeritus of the University of Tokyo President of Japan Society of Maintenology (JSM) http://www.jsm.or.jp/jsm/en/index.html Editor in Chief of E-Journal of Advanced Maintenance (EJAM) http://www.jsm.or.jp/ejam [email protected]

Hassane Mohellebi Electrical Engineering Laboratory Tizi-Ouzou University BP17RP 15000 Tizi-Ouzou Algeria [email protected]

Lech Napierała Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Yoshihiro Nishimura National Institute of Advanced Industrial Science and Technology 1-2-1 Namiki 305-8564 Tsukuba Japan [email protected]

Youngmin Park Chosun University Seosukdong 375 501-759 Gwangju Korea [email protected]

Jozsef Pavo Budapest University of Technology and Economics Goldman Gy. tér 3 1111 Budapest Hungary [email protected]

Cuixiang Pei Uesaka-Demachi Laboratary, The University of Tokyo 2-11-16, Yayoi, Bunkyoku 113-0032 Tokyo Japan [email protected]

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Matthias Pelkner BAM Federal Institute for Materials Research and Testing Unter den Eichen 87 12205 Berlin Germany [email protected]

Tomasz Pietrusewicz Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Denis Prémel CEA List Centre Saclay; Bât 611 PC120 91191 Gif-sur-Yvette France [email protected]

Grzegorz Psuj Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Joao Rebello Federal University of Rio de Janeiro Ilha do Fundao CT Room F-210 21941-972 Rio de Janeiro Brasil [email protected]

Verena Reimund BAM Federal Institute for Materials Research and Testing Unter den Eichen 87 12205 Berlin Germany [email protected]

Maciej Roskosz Silesian University of Technology ul. Akademicka 2A 44-100 Gliwice Poland [email protected]

Guglielmo Rubinacci Università degli Studi di Napoli Federico II Via Claudio 21 80125 Naples Italy [email protected]

Yasutomo Sakai Tohoku University 6-6-01-2, aramaki aza aoba, aoba ward 980-8579 Sendai Japan [email protected]

Adriana Savin National Institute of Research and Development for Technical Physics 47 D. Mangeron 700050 Iasi Romania [email protected]

Hans-Peter Schmidt UAS Amberg Weiden (HAW) Kaiser Wilhelm Ring 23 D-92224 Amberg Germany [email protected]

Karl Schmidt Evisive, Inc., 8867 Highland Road, #378, Baton Rouge, Louisiana, 70808 USA [email protected]

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Jan Sikora Lublin University of Technology Electrical Engineering and Computer Science Faculty 20-618 Lublin 38A Nadbystrzycka Str. Poland [email protected]

Ryszard Sikora Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Christian Seibold UAS Amberg Weiden (HAW) Kaiser Wilhelm Ring 23 D-92224 Amberg Germany [email protected]

Kisu Shin Korea Nationa Defense University 205 Susaek-dong 122-875 Seoul Korea [email protected]

Marek Smaga University of Kaiserlautern Gottlieb-Daimler-Straße 67663 Kaiserlautern Germany [email protected]

Milan Smetana DEBE, Faculty of Electrical Engineering, University of Žilina Univerzitná 1 SK-01026 Žilina Slovak Republik [email protected]

Thierry Sollier IRSN 31, av. de la Division Leclerc BP 17 92262 Fontenay-aux-Roses France [email protected]

Krzysztof Stawicki Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Tatiana Strapáčová DEBE, Faculty of Electrical Engineering, University of Žilina Univerzitná 1 SK-01026 Žilina Slovak Republik [email protected]

Barbara Szymanik Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Toshiyuki Takagi Tohoku University Katahira 2-1-1, Aoba-ku 980-8577 Sendai Japan [email protected]

Antonello Tamburrino University of Cassino V.G. Di Biasio, 43 03043 Cassino Italy [email protected]

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Theodoros Theodoulidis University of Western Macedonia Bakola & Sialvera 50100 Kozani Greece [email protected]

Tetsuya Uchimoto Tohoku University 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577 Sendai Japan [email protected]

Lalita Udpa Michigan State University 2100C Engineering Building 48824-1226 East Lansing USA [email protected]

Satish S. Udpa Michigan State University 3410 Engineering Building 48824-1226 East Lansing USA [email protected]

Elmar van den Elzen Lismar Engineering BV Ambachtenstraat 55 1191JM Ouderkerk a.d. Amstel Netherlands [email protected]

Vertesy Gabor Research institute for Technical Physics and Materials Science Konkoly Thege Miklós ut 29-33 H-1121 Budapest Hungary [email protected]

Xie Shejuan Tohoku University 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577 Sendai Japan [email protected]

Katsuhiko Yamaguchi Fukushima University 1 Kanayagawa 960-1296 Fukushima Japan [email protected]

Toshihiro Yamamoto JAPEIC 14-1 Benten-cho, Tsurumi-ku 230-0044 Yokohama Japan [email protected]

Noritaka Yusa Tohoku University 6-6 Aramaki, Aza Aoba Aoba, Sendai 980-8579 Miyagi Japan [email protected]

Marcin Ziółkowski Department of Electrical Engineering West Pomeranian University of Technology, Szczecin ul. Sikorskiego 37 70-313 Szczecin Poland [email protected]

Chiara Zorni CEA Saclay Centre Saclay; Bât 611 PC120 91191 Gif-sur-Yvette France [email protected]

Marek Ziółkowski Ilmenau Univeristy of Technology Helmholtzplatz 2, P.O.Box 100565 98684 Ilmenau Germany [email protected]

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Contents Preface T. Chady, S. Gratkowski, T. Takagi and S.S. Udpa Conference Organization List of Participants

v vii ix

Keynote Lecture Pipe Wall Thickness Inspection with Current Driven Thermal Method Satoshi Honda

3

Modeling and Inverse Problems Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection G. Yang, Z. Zeng, L. Udpa and S.S. Udpa Non-Iterative MUSIC-Type Algorithm for Eddy-Current Nondestructive Evaluation of Metal Plates Tommy Henriksson, Marc Lambert and Dominique Lesselier Identification of Defects in 3D Space Using Computer Radiography System Wojciech Chlewicki, Piotr Baniukiewicz, Tomasz Chady and Andrzej Brykalski A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole S.K. Burke Magnetic Response Field of Spherical Defects Within Conductive Components M. Kreutzbruck, H.-M. Thomas, R. Casperson, V. Reimund and M. Pelkner Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking from Eddy-Current Signals Ladislav Janousek, Milan Smetana and Marcel Alman Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition Konstanty M. Gawrylczyk Metamodel as Input of an Optimization Algorithm for Solving an Inverse Eddy-Current Testing Problem Rémi Douvenot, Marc Lambert and Dominique Lesselier Fast Multipole Method for 3D Electromagnetic Boundary Integral Equations. Application to Non Destructive Testing on Complex 3D Geometries Tekoing Lim, Gregoire Pichenot and Marc Bonnet Computation of the Magnetostatic Field in Nonlinear Media via the Integral Equation Formalism: Application to the Characterization of Magnetic Flux Leakage NDT System Emna Amira Fnaiech, Denis Prémel, Claude Marchand and Bernard Bisiaux Efficient Computation of Eddy Current Crack Signals Theodoros Theodoulidis

13

22 30

36 44

53 61

71

79

87

96

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Experimental Validation of a Fast Non-Iterative Imaging Algorithm for Eddy Current Tomography Salvatore Ventre, Flavio Calvano, Guglielmo Rubinacci and Antonello Tamburrino Numerical Evaluation of Microwave Testing for Pipe Thinning Yasutomo Sakai, Noritaka Yusa and Hidetoshi Hasizume Parallelization of Crack Signal Calculation Using CUDA Imre Kiss, József Pávó and Szabolcs Gyimóthy Electromagnetic-Acoustic Transducers Modeling in Time Domain Using the Finite Element Method Marcin Ziolkowski and Stanislaw Gratkowski Eddy Current Testing of Ferromagnetic Materials: Modelling of Flaws in a Planar Medium Chiara Zorni, Christophe Reboud, Marc Lambert and Jean-Marc Decitre Efficient Propagation of Uncertainty in Simulations via the Probabilistic Collocation Method Jeremy S. Knopp, John C. Aldrin and Mark P. Blodgett Computation of the Magnetic Field Due to a Defect Embedded in a Planar Stratified Media: Application to AC Field Measurement Techniques Denis Prémel and Grégoire Pichenot Automatic Detection and Identification of Image Quality Indicators in Radiograms Piotr Baniukiewicz and Ryszard Sikora Numerical Simulation of Acoustoelastic Effect in Pre-Stressed Media Cuixiang Pei and Kazuyuki Demachi “BEMLAB” – Universal, Open Source, Boundary Element Method Library Applied in Micro-Electro-Mechanical Systems Paweł Wieleba and Jan Sikora Use of Half-Analytical Method for the Detection of Defects in Diet Pulses Hassane Mohellebi, Ferroudja Bouali and Mouloud Feliachi Imperialist Competitive Algorithm Applied to Eddy Current Nondestructive Evaluation Ammar Hamel, Hassane Mohellebi and Mouloud Feliachi

103

111 117

125

134

141

149

157 164

173 183

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Transducers and Techniques Pulsed ECT Method for Evaluation of Pipe Wall-Thinning of Nuclear Power Plants Using Magnetic Sensor Shejuan Xie, Toshihiro Yamamoto, Toshiyuki Takagi and Tetsuya Uchimoto Developing ECT System with AMR Sensor for Combustion Chamber Dongfeng He, Mitsuhara Shiwa, Jianping Jia, Hisashi Yamawaki, Ichizo Uetake, Junji Takatsubo, Shinichi Moriya and Koichi Okita Flux Leakage Measurements for Defect Characterization Using NDT Adapted GMR Sensors Matthias Pelkner, Andreas Neubauer, Mark Blome, Verena Reimund, Hans-Martin Thomas and Marc Kreutzbruck

203

211

217

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Evaluation of EMAT Signals Using Magnetostrictives for Imaging Yoshihiro Nishimura, Akira Sasamoto and Takayuki Suzuki Pulsed Eddy Current Testing – Application to Defect Evaluation Milan Smetana, Ladislav Janousek, Klara Capova and Maria Michniakova An ECT Probe with Widely Spaced Coils for Local Wall Thinning in Nuclear Power Plants Toshihiro Yamamoto, Tetsuya Uchimoto and Toshiyuki Takagi PLL Based Eddy Current Measuring System for Inspection of Outer Flaw in Titanium Alloy Plate Tomasz Chady, Jacek Kowalczyk, Leon Nawos-Wysocki, Grzegorz Psuj and Ireneusz Spychalski Giant Magneto-Resistive Sensor Based Magnetic Flux Leakage Technique for Inspection of Track Ropes W. Sharatchandra Singh, B.P.C. Rao, S. Mahadevan, T. Jayakumar and Baldev Raj

225 233

241

249

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Application of Electromagnetic Nondestructive Techniques Pipe Wall Thickness Measurement by Electro-Magnetic Acoustic Transducer Using Band Exciting Method Daigo Kosaka, Fumio Kojima and Kosuke Umetani Applicability of Magnetic Flux Leakage Method for Wall Thinning Monitoring in Nuclear Power Plants Hiroaki Kikuchi, Isamu Shimizu, Katsuyuki Ara, Yasuhiro Kamada and Satoru Kobayashi Stress Corrosion Cracks Evaluation in 316 Austenitic Stainless Steel Plate Tomasz Chady, Jacek Kowalczyk and Grzegorz Psuj Multi-Frequency Eddy Current NDE of the Distance Between Parts in Aeronautical Assemblies Thanh Long Cung, Pierre Yves Joubert and Eric Vourc’h Artificial Heart Valve Testing Using Electromagnetic Method Tatiana Strapacova, Klara Capova, Ladislav Janousek and Milan Smetana Conceptual Design of an Industrial System for Automatic Radiogram Analysis Ryszard Sikora, Tomasz Chady, Piotr Baniukiewicz, Marcin Caryk, Przemysław Łopato, Lech Napierała, Tomasz Pietrusewicz and Grzegorz Psuj

267

275

282

288 296 302

Material Characterization Quantification of Sigma Phase Precipitation by Magnetic Non Destructive Testing João M.A. Rebello, Rodrigo Sacramento, Maria C.L. Areiza and K. Santos de Assis Nondestructive Characterization of Neutron Induced Embrittlement in Nuclear Pressure Vessel Steel Microstructure by Using Electromagnetic Testing I. Altpeter, G. Dobmann, G. Hübschen, M. Kopp and R. Tschuncky

311

322

xx

In-Line Thin Film Characterization Using Eddy Current Techniques Susanne Hillmann, Marcus Klein and Henning Heuer Feasibility of Stress State Assessment on the Grounds of Measurements of the Strength of the Residual Magnetic Field of Ferromagnetics Maciej Roskosz Magnetic Characterization of Material Degradation Using Dynamical Minor Loops Satoru Kobayashi, Shinichi Tsukidate, Hiroyuki Okazaki, Yasuhiro Kamada, Hiroaki Kikuchi and Toshihiro Ohtani Local Magnetic Properties and Magnetic Particle Distribution Due to Cr Depletion in Sensitized Ni Based Alloy K. Yamaguchi, K. Suzuki, T. Takase, T. Takara, O. Nittono, T. Uchimoto and T. Takagi Metamaterials in Electromagnetic Nondestructive Evaluation Adriana Savin, Rozina Steigmann, Alina Bruma, Nicoleta Iftimie and Raimond Grimberg Evaluation of Plastic Deformation in Steels by Magnetic Hysteresis Measurements Gábor Vértesy, Shuzo Ueda, Tetsuya Uchimoto, Toshiyuki Takagi, Ivan Tomáš and Zofia Vértesy

330

339

347

355

362

371

High Frequency Techniques and Others GPR for UXO Recognition Raimond Grimberg, Adriana Savin, Nicoleta Iftimie, Sorin Leitoiu and Aurel Andreescu Application of Microwave Interferometry in Complex Engineered Dielectric Materials Karl Schmidt and Jack Little Detection of Concealed, Graphite Containing Frescos, Using Microwave Enhanced Infrared Thermography Paweł Lesiecki and Barbara Szymanik Solid Materials Complex Permittivity and Inhomogenities Determination in High Frequency Range Dagmar Faktorová Terahertz Time Domain Inspection of Composite Coatings for Corrosion Protection Przemyslaw Lopato, Tomasz Chady and Joao M.A. Rebello Simulation Assisted Diagnostic of Switching Arcs Hans-Peter Schmidt, Michael Anheuser and Sylvio Kosse Studies on Analysis Technique of Commutation Phenomena for Cleaner’s Universal Motor Using the State Variable Method Yuji Akiyama and Yuta Niwa Propositions for the Analysis of Commutation Phenomena of Universal Motors Using the State Function Method Yuji Akiyama and Yuta Niwa

381

389

402

410

417 425

432

439

xxi

Detection of CFRP’s Degradation Through Electromagnetic Procedures Bogdan Serghiac, Daniel Petrica Salavastru, Paul Doru Barsanescu, Adriana Savin, Rozina Steigmann and Raimond Grimberg Microwave Antenna Sensors for Fatigue Crack Monitoring Under Lap-Joints Justin Erdmann and Haiying Huang Subject Index Author Index

447

456 467 471

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Keynote Lecture

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-3

3

Pipe Wall Thickness Inspection with Current Driven Thermal Method Satoshi HONDA a,1 a

Faculty of Science & Engineering, Keio University, Japan

Abstract. Electric potential difference(EPD) method is widely used for diagnosing and monitoring flow conduits. Theoretical analysis and the exact solution of the electrical potential field in pipe wall have been given, and 2D approximation is effective for small pipe wall thickness there. This study proposes to use temperature distribution driven by Joule heat with the electric current other than electrical potential difference. Under thin wall approximation, 2D electric and thermal problems are analyzed and exact solutions are given. Keywords. Nondestructive test, pipe wall thinning, forward analysis, electric potential difference

Introduction Electric potential difference(EPD) method is widely used for diagnosing and monitoring flow conduits [1]. It applies large electric currents between a pair of electrodes on pipe wall surface, and the electrical potentials are measured with multiple potential electrodes. Since the localized pipe wall thinning or a wall crack deforms the potential field, we can monitor and/or diagnose pipe wall condition under test. The method is also required to evaluate pipe wall thinning in larger span. We have studied the prospect of the method to evaluate pipe wall thinning. Based on the work on non-intrusive resistance thermometer for fast breeder reactor[2,3], theoretical analysis and the exact solution of the electrical potential field in pipe wall have been proposed[4], and 2D approximation is effective for small pipe wall thickness. We propose in the paper to use temperature distribution driven by Joule heat with the electric current other than electrical potential difference. Under thin wall approximation, 2D electric and thermal problems are analyzed and exact solutions are given. 1 Corresponding Author: Satoshi Honda, Faculty of Science & Technology, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan; Email: [email protected]

4

S. Honda / Pipe Wall Thickness Inspection with Current Driven Thermal Method

1. Analysis of Wall Potential Problem for EPD Method 1.1. 3D Analysis Let the electric potential inside the fluid be φ1 (ρ, ϕ, z), and the one inside the pipe wall, φ2 (ρ, ϕ, z), where cylindrical coordinates are adopted with pipe axis as z coordinate. Electrical current is fed between a pair of rectangular electrodes of bw×bw on the outer surface (b, 0, 0). If we let σ1 and σ2 be electrical conductivities of the fluid and the pipe wall, the following potential problem is formulated. Δφ2 = 0,

a<ρ
(1)

Δφ1 = 0, ρ
(2) (3) (4)

where rect(·; ·) denotes the rectangular shape of the electrodes  rect(x; w) 

1, |x| ≤ w/2 0, |x| > w/2

(5)

and i0 , the driving current density. In order to solve the problem, we introduce the potential distribution φ0 for the bulk cylinder of the radius b: Δφ0 = 0,  i0 ∂φ0  = − rect(ϕ; w) rect(z; bw),  ∂ρ ρ=b σ2

ρ
(6) (7)

This potential φ0 is obtained by using Green’s function G(ρ, ϕ, z; ρ , ϕ , z  ) corresponding to this Neumann problem which satisfies, 1 ΔG = −δ(ρ − ρ ) δ(ϕ − ϕ )δ(z − z  ), ρ   ∂G  =0 ∂ρ ρ =b

(8) (9)

The Green’s function is given as, G(ρ, ϕ, z; ρ , ϕ , z  ) =

  ∞ ∞   Km m (λb)    I K cos m(ϕ − ϕ ) · (λρ ) − (λρ ) m  (λb) m 2π 2 Im 0 m=0 ·Im (λρ) · cos λ(z − z  ) dλ (10)

S. Honda / Pipe Wall Thickness Inspection with Current Driven Thermal Method

5

where Im (·) and Km (·) denote m-th order modified Bessel functions of first and second kinds, respectively, and m , Neumann factor. This Green’s function gives the potential φ0 for the simplified model:  i0 G(ρ, ϕ, z; b, ϕ , z  ) · rect(ϕ ; w) rect(z  ; bw)bdϕ dz  φ0 = σ 2 S

  ∞ ∞   bw i0 m Im (λρ) mw · · cos λz sinc λ dλ, = cos mϕ sinc  (λb) σ2 m=0 2π 2 2 λbIm 2 0 (11) Due to the linearity of the original potential problem, we assume the following solution: φ2 = φ0 + φ˜2 = φ0 + φ1 =

 ∞ ∞  m cos mϕ · [dm Km (λρ) + cm Im (λρ)] cos λz dλ, 2π 2 0 m=0

 ∞ ∞  m cos mϕ fm Im (λρ) cos λz dλ 2π 2 0 m=0

(12)

(13)

Since φ0 has already accounted for the current feeding electrodes, the boundary condition for the potential φ˜2 reads as follows:  ∂ φ˜2  = 0. (14)  ∂ρ  ρ=b

From three boundary conditions (4) and (14), we obtain three independent equations for the coefficients cm , dm , fm of series expansions, which evaluate the coefficients. When we put a pair of current feeding electrodes on ϕ = 0, π, the exact form of the potential distribution is,   ∞  1 Am (λ) Im (λρ) + · Wm (λ) cos λz dλ cos mϕ (15) φ2 =  (λb) π2 λbIm Bm (λ) 0 m:odd      κ  σ−1 Km (λb) Im (λa) · Km (λρ) −  Im (λρ) (16) Am (λ)  − Im (λa) + b λb Im (λb)   Im (λa)     Bm (λ)   + κλ · [Im (λb)Km (λa) − Im (λa)Km (λb)] Im (λa)   (λb) − Im (λb)Km (λa)] + σ [Im (λa)Km

(17)

1.2. Application to Evaluation of Pipe Wall Thinning For the convenience, let us normalize the variables here in order to evaluate surface potential, as ξ  λb, α  a/b.. In the limit case of the conductivities being

6

S. Honda / Pipe Wall Thickness Inspection with Current Driven Thermal Method

0 ≈ σ1  σ2 and of very thin pipe wall, the potential distribution on the wall reduces to,

 z  mw  ∞ i0  2 ξw cos ξ dξ cos mϕsinc Q (ξ) sinc φ2 (b, ϕ, z) = m σ2 b π2 2 2 b 0 m:odd

(18) Qm (ξ) 

I  (ξα) 1 Im (ξ) − 2m  ·    (ξ) − K  (ξ)I  (ξα) ξIm (ξ) ξ Im (ξ) Km (ξα)Im m m

(19)

b−a = 1 − α is small, dropping higher order term of in Taylor series Since  b expansion of each function of Qm gives the following simplification. Qm (ξ) = =

  Im 1 Im (ξ) (ξ) − ξIm (ξ) − ·  (ξ)  (ξ)  (ξ)I  (ξ) − K  (ξ)I  (ξ)] ξIm ξ 2 Im ξ [Km m m m

a 1 1− = · 2 2 2 (ξ + m ) b − a ξ + m2

(20)

At the reduction to this final form, we have adopted formulas for modified Bessel functions. From Eq.(20), the surface potential distribution is also reduced to, φ2 (b, ϕ, z) =

 mw i0 a 2  · · 2 cos mϕ sinc b − a b σ2 π 2 m:odd  ∞ z  w 1 cos ξ dξ sinc ξ ξ 2 + m2 2 b 0

(21)

Let the pipe wall thickness be t  b − a. If we make the size w of the current feeding electrode infinitesimally small, sinc(·, w) approaches to unity. Therefore, in this limit case surface potential can be evaluated as follows.  ∞ z 2  i0 1 · 2 ξ dξ φ2 (b, ϕ, z) = cos mϕ cos 2 2 σ2 t π ξ +m b 0 m:odd z cosh − cos ϕ i0 1  zb (22) · log = 4π σ2 t + cos ϕ cosh b The denominator, σ2 t, implies that we can model thinning pipe wall as the region with reduced conductivity. Consequently, reduced 2-D problem can be analyzed in the complex plane, Z = X + iY,

z → X,

bϕ → Y

(23)

The following conformal mapping

 Z ζ = exp , b

Z = b log ζ

(24)

7

S. Honda / Pipe Wall Thickness Inspection with Current Driven Thermal Method 

 

φ/π



 

























z/b

Figure 1. Complex potential evaluation for symmetric excitation Fs (Z).

transforms cylindrical surface of pipe, 0 ≤ ϕ ≤ 2π, to whole complex ζ−plane. And hence, 2D potential distributions on the circular cylinder can be easily obtained by analytic functions in whole plane as complex potentials. Since current feeding electrodes are represented by electric charges with corresponding polarities, log(ζ ±1) reproduces 2D approximation of 3D exact solution to wall potential distributions in Eq.(22). Fig.1 shows current field streamlines on the pipe wall, where a pair of current electrodes are set at (−4b, 0) : (4b, 0), and the corresponding analytic function is

 Z − 4b sinh b

 (25) Fs (Z) = log Z + 4b sinh b From the figure, we conclude that the current distribution is uniform in the region far from the current feeding electrodes.

2. Thinning Pipe Evaluation with Joule Heating Joule heat generated by the driving current varies with wall pipe thickness, or conductivity. Thus the resulting temperature distribution changes with the wall thickness. In order to analyze the resulting temperature distribution, Joule heat distribution is modeled beforehand. We model the thinning wall region as small circle with the radius of a at the origin in whole 2D plane far from the current feeding electrodes. Then Joule heat distribution is obtained from the following 2D potential problem: Δφ1 = 0, Δφ2 = 0, φ1 |r=a = φ2 |r=a ,

a
(26) (27) (28)

where the same symbols φ1 , φ2 as in the previous section are used for describing the electric potentials on the infinite 2D plate. As in the case of 3D analysis, we

8

S. Honda / Pipe Wall Thickness Inspection with Current Driven Thermal Method

expand the potentials in series of ( ar )±n , cos nθ, sin nθ, and the boundary conditions determine the coefficients of the series expansion to give the following simple solutions. φ1 = −E0 r cos θ − φ2 = −

1−σ a2 E0 cos θ + c0 , 1+σ r

2 E0 r cos θ + c0 , 1+σ

r≥a

(29)

r
(30)

The resulting Joule heat reads, P1 = j 1 · E 1 = σ1 (−grad φ1 ) · (−grad φ1 ) 2 4

1 − σ a2 1−σ a 2 , 2 cos 2θ + = σ1 E0 1 − 1 + σ r2 1+σ r4 P2 = j 2 · E 2 = σ2 (−grad φ2 ) · (−grad φ2 ) = σ1 E02

4σ , (1 + σ)2

(31) (32)

This Joule heat generates the temperature distribution u according to the following heat transfer equation: ∂u = α2 Δu − β 2 u + κP˜ ∂t

 4 a2 2 2 a ˜ P = H(r − a)P0 σ ˜ −σ ˜ 2 2 cos 2θ + σ ˜ 4 , r r

(33) (34)

where H(·) denotes Heaviside function and σ ˜  (1 − σ)/(1 + σ). In order to avoid divergent solution, the second term in the right hand side of Eq.(33) is introduced and the origin of the temperature is shifted to simplify the third term by linearity. The Green’s function satisfying the following differential equation 

β2 1 ∂ − G(r, t ; r  , t ) = −δ(r − r  ) δ(t − t ) (35) Δ− 2 α ∂t α2 is given by G = H(t − t )

 1 r2 − 2rr cos(θ − θ ) + r2 2  · exp −β . (36) (t − t ) − 4π(t − t ) 4α2 (t − t )

By using this Green’s function, we obtain the temperature distribution as the three-fold integration with respect to t , θ , r , as follows:  t

2π



∞

u(r, θ, t) = 0

0

0

G(r, t ; r  , t ) κP˜ r dr dθ  dt

 r2 − 2rr cos(θ − θ ) + r2 κP0 2  · exp −β (t − t ) − = 4π(t − t ) 4α2 (t − t ) 0 0 a

 a2 a4 · σ ˜2 − σ ˜ 2 2 cos 2θ + σ ˜ 2 4 r dr dθ  dt (37) r r  t

2π



∞

9

S. Honda / Pipe Wall Thickness Inspection with Current Driven Thermal Method

We start the evaluation of the outermost integration with respect to t . The factor relating to the variable t is picked up and defined as T (t): 

t

T (t) = 0

γ



γ 1 2  dt exp −β (t − t ) − 4π(t − t )α2 t − t

(38)

1 (r2 − 2rr cos(θ − θ ) + r2 ) 4α2

Since the stationary state is of main interest, we evaluate the integration with t to infinity and change the variable p = t − t :

 γ 1 1 √ exp −β 2 p − dp = 2K0 (2β γ) 2 p p 4πα 0

 β 2 1   2 K0 . r − 2rr cos(θ − θ ) + r = 2π α

T (∞) =

1 4πα2



∞

(39)

In order to evaluate the remaining integrals, let us normalize the variables: β β  β  ¯. Then the integration comes to, α r = ρ, α r =ρ , α a=a u∞ (r, θ)  u(r, θ, ∞) =





 κP0 2 − 2ρρ cos(θ − θ  ) + ρ2 K ρ 0 2πβ 2 0 a ¯

 a ¯2 ¯4 2  2 a · σ ˜ −σ ˜  2 2 cos 2θ + σ ˜  4 ρ dρ dθ  (40) ρ ρ 2π

∞

Since the addition theorem holds for modified Bessel function:

K0



ρ2 − 2ρρ cos(θ − θ ) + ρ2

⎧ ∞  ⎪  ⎪ ⎪ Kn (ρ)Jn (ρ ) ein(θ−θ ) ⎪ ⎨

=

(|ρ| ≥ |ρ |)

n=−∞

∞  ⎪  ⎪ ⎪ Kn (ρ )Jn (ρ) ein(θ−θ ) ⎪ ⎩

(|ρ | ≥ |ρ|)

n=−∞

(41) integration with respect to θ remains only for n = 0, ±2. And finally, after the evaluation of the last integral with respect to ρ , we obtain, u∞ (r, θ) =



 ∞ 1 1 2 3   κP σ ˜ a ¯ J (ρ) K (¯ a ) + a ¯ K (ρ )dρ 0 0 1 0 β2 ρ 3 a ¯ −

1 κP0 σ ˜ 2¯ a2 cos 2θJ2 (ρ)K1 (¯ a), β2

(r < a)

(42)

10

S. Honda / Pipe Wall Thickness Inspection with Current Driven Thermal Method



 ∞ 1 1 2 3   u (r, θ) = 2 κP0 σ ˜ a ¯J0 (ρ) K1 (ρ) + a ¯ K0 (ρ )dρ β ρ 3 ρ ∞

1 κP0 σ ˜ 2¯ a2 cos 2θJ2 (ρ)K1 (ρ) β2 

 ∞ 1 1 2 4   ˜ K0 (ρ) · a ¯J1 (¯ a) − ρJ1 (ρ) + a ¯ J0 (ρ )dρ + 2 κP0 σ β ρ 3 a ¯

 1 1 1 2 J1 (¯ ˜ 2¯ a cos 2θK2 (ρ) a) − J1 (ρ) , (r ≥ a) (43) − 2 κP0 σ β a ¯ ρ −

An example shape of the Joule heat distribution is shown in Fig.2(a), and the corresponding temperature distribution, in Fig.2(b).

Figure 2. Stationary temperature and heat distributions are numerically evaluated from Eqs.(42) & (43).(a)Joule heat distribution. (b)3D plot. First quadrant is shown due to the symmetry.

3. Conclusion We have presented the analytical solution for temperature distribution driven by Joule heat over the pipe wall. This exact solution of the forward problem with the local wall thinning is effective and applicable to wide range diagnosis of pipe wall anomaly. It, however, should be concidered the effect of mass reduction to heat conduction, which was neglected in the formulation.

References [1] [2]

[3] [4]

A. M. Pritchard and P. Webb Use of the FSM Technique in the Laboratory to Measure Corrosion Inhibitor Performance in Multiphase Flow Proc. CORROSION/98, paper no.8 H. Yamasaki, S. Honda, M. Ueda, A. Endou, M. Fueki A Novel Non-intrusive Resistance Thermometer for Fast Breeder Reactor Proc. SICE2003 Annual Conf. Fukui pp 519 / 523(2003) H. Yamasaki, S. Honda, M. Ueda, A. Endou, M. Fueki A Novel Non-intrusive Resistance Thermometer for Fast Breeder Reactor Trans. SICE, vol.43, No.9, pp 756 / 761(2007) S.Honda Thinning Pipe Wall Evaluation by using Electric Potential Difference Method Proc. SICE2008 Annual Conf. Tokyo pp 520 / 529(2008)

Modeling and Inverse Problems

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-13

13

Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection 1

G. YANG1,Z. ZENG 2,L. UDPA1*, and S. S. UDPA1 Department of Electrical & Computer Engineering, Michigan State University, East Lansing, Michigan 48824, U.S.A2 Department of Aeronautics, Xiamen University, Xiamen, Fujian 361005, China

Abstract. In any NDE application, the availability of a theoretical model is very useful in understanding the capability of the system since it can enable the visualization of field/flaw interaction for different flaw and sensor geometries. A numerical model capable of simulating inspection of multi layered structures using eddy current excitation and magneto resistive sensing is developed to predict 2D image data of rivet locations. The model is used to study particularly the effect of sensor tilt on the probability of detection (POD) of defects at rivet sites. The modeling of sensor tilt during inspection around rivet sites has to take into account finite source coil and meshing of the finite source coil at each scan position. This paper presents a finite element (FE) model formulation using reduced magnetic vector potential and electric scalar potential in a way that does not require meshing source coils. In addition to simulating the effect of sensor tilt on the signal, this paper also describes features in the signal that are invariant to sensor tilt but sensitive to defect parameters. Keywords. Eddy current, Giant magnetoresistive sensor, sensor tilt, multi layered structure

Introduction The detection of hidden cracks around fastener sites in multi-layered structures poses a major challenge in the aviation industry [1]. Although, eddy current testing methods have been used extensively in this application, the skin depth or penetration depth of the fields has limited their use in detecting 2nd and 3rd layer defects under fastener heads. With the development of magnetoresistive (MR) sensors, eddy current inspection system combined with MR sensors is finding increasing use in detecting directly the magnetic field associated with the induced currents. An eddy current - giant magnetoresistive (GMR) sensor system has been developed and shown to be effective in detecting subsurface cracks in a multilayer structure. A schematic of the sensor, with linear multiline currents and GMR sensor on the line of symmetry, is shown in Figure 1. In the presence of fasteners and/or cracks, a non-zero normal magnetic field is produced at the center of the source coil and is picked up by the GMR sensor. The GMR signal comprises measurement of normal component of magnetic flux density associated with induced eddy currents in the sample [2].

*

Corresponding Author: [email protected]

14

G. Yang et al. / Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection

Figure 1. The EC GMR sensor: (a) the excitation coil with a GMR sensor and the tested sample; (b) schematic of operation of sensor for crack detection.

In a practical inspection scenario, variations in several experimental parameters such as lift off, top and bottom layer conductivity, edge effect can alter the measured signal and hence the POD of a subsurface defect. This paper presents the modeling of defect signals in the presence of sensor tilt during the measurement process. Further the signals generated are used to derive discriminatory features that enhance the detection probability of subsurface defects in the presence of sensor tilt. The detection of detects based on the asymmetry of two lobes of the rivet signal using model-based methods has been reported in [3-4]. In these studies, the source current is modeled as an infinite coil, obviating the need for modeling the scanning operation which is a time intensive process. However modeling of sensor tilt is rendered complex because of the need to model a finite source coil and the re-meshing at each scan position of the sensor. This paper presents the application of a finite element formulation using reduced magnetic vector potential and electric scalar potential [5-6] for simulating the multiline coil motion across the sample without re-meshing the source coil which results in significant computational savings. The feature based defect detection and classification using multi-component signal features that are insensitive to sensor-tilt effect validate the EC - GMR sensor system for the application considered.

1. Numerical Model and Sensor-tilt Parametric Study

1.1 System and Test Geometry A multi-line coil producing uniform eddy current across the test rivet structure, sketched schematically in Fig. 1 (a), is employed as the current source. In the absence

G. Yang et al. / Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection

15

of any discontinuity, the symmetry of the coil geometry results in zero normal component of magnetic field at the line of symmetry on the center of the source coil. In the presence of a rivet and/or crack, the uniform magnetic field is distorted to yield the nonzero normal component response. A GMR sensor is placed at the center location to measure this normal flux density Bz due to the perturbation in induced current. The analysis of nonzero signal measured by the GMR sensor can be used to detect and characterize cracks around rivet sites. The sample consisting of three aluminum layers riveted together is studied in this paper. The rivets are drilled through three layers and cracks of different sizes are machined in the 3rd layer plate around rivet sites. A single frequency excitation current is applied to the multi-line coil and the changes in magnetic field are collected by the GMR sensor.

1.2 Reduced Vector Potential Formulation based Numerical Model Finite element formulation of 3-D eddy current testing problems is typically based on magnetic vector potential A and electric scalar potential V. However this formulation requires generating a mesh for the excitation foil/coil together with the test sample and the domain has to be remeshed for each coil position. This can result in excessive computation time and error. Finite element model based on a formulation using the reduced magnetic vector potential and the electric scalar potential ( Ar − V − Ar formulation) has been proposed to simulate the EC-GMR inspection signals [5-6]. The advantage of this formulation is that the source coil is not meshed and hence there is no need for re-meshing the source current during scanning. The mesh and system matrix remain unchanged with different coil motion. The implementation of the system matrix pre-conditioner is performed only once during the entire scan. The formulation model defines the reduced magnetic vector potential by the decomposition of the magnetic flux density B into two parts: B = Bs + Br = μ0 H s + Br (1) where Bs and Hs are the flux density and field density due to the source in free space, and Br is the flux density due to induced current or magnetization. Considering the field equations together:

∇ ⋅ Bs = 0 , ∇ × A s = Bs ,

∇ × Hs = Js , ∇ × A r = Br

∇ ⋅ Br = ∇ ⋅ B − ∇ ⋅ Bs = 0 , (2)

The magnetic vector potential A is correspondingly decomposed into As and Ar where As is the vector potential in air due to excitation current and Ar is the vector potential due to induced and/or magnetization currents. Generally, Hs and As can be evaluated by Biot-Savart’s law. Hs is calculated by

Hs =

1 4π

³

Ω′

J s (r′) ×

r − r′ dΩ 3 r − r′

(3)

16

G. Yang et al. / Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection

The magnetic vector potential As is:

As =

μ0 4π

J s (r′) dΩ Ω′ r − r′

³

(4)

where Ω′ is the volume of the current source; μ0 is the free-space permeability. r and r ′ denote the coordinates of observation and source points, respectively. Correspondingly, the governing equations using this formulation can be written as:

ν∇ 2 A r + jωσ A r + σ∇V = (1 − vr )∇ × H s − jωσ A s ∇ ⋅ ( jωσA r + σ∇V ) = −∇ ⋅ jωσA s

(5)

Note that the weak form of (5) is written as

³ (∇N ⋅ jωσA + ∇N ⋅σ∇V )dΩ + ³ N [− jωσ (A = − ³ ∇N ⋅ jωσ A dΩ i

Ω

Ω

r

i

i

Γ

s

i

r

+ A s ) − σ∇V ]⋅ nˆ dΓ (6)

= 1,2, N with N the number of nodes) are shape functions, Ω the ˆ the unit outward normal vector of Γ. By solution domain, Γ conductor surface, and n

where N i ( i

neglecting the surface integral in (6), we implicitly set the normal component of induced currents on conductor surface to 0. The cost of the new formulation is that besides materials and

H s , ∇ × H s in presence of magnetic

A s must be evaluated. However, evaluating these analytical values takes

much less time than that required for performing the incomplete factorization in each coil position. The model has been validated by comparing model predicted signal and experimental signal as shown in Figure 2. The Figure 2 (a) presents the model validation in terms of defective rivet detection. The geometry of this sample is two layers (6mm and 4mm thickness) with a 2nd layer radial crack of length 5mm at a rivet site. The 1D signal measured in a scan across the rivet in X direction is plotted and the same trend and asymmetry is observed in both simulated and experimental signals. The Figure 2 (b) presents validation of the model for a cylindrical geometry; air core pancake probe inspection of a tube with an OD axial notch at 100KHz single frequency excitation.

G. Yang et al. / Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection

17

1 0.9 0.8 0.7 0.6

(a)

0.5 0.4 0.3 0.2 0.1 0 -6

-4

-2

0

2

Numerical 1D scan Experimental 1D scan 4 6

(b)

Figure 2. Model validation: comparison of 1D model simulated signal (red) with experimental measurement (blue) (a) 3rd layer crack in multilayer sample (b) OD axial notch in a tube.

2. Simulation Results and Feature-based Crack Detection

2.1 Sensor-tilt Parametric Study The FE model using reduced vector potential formulation was used to conduct a systematic study of the effect of increasing sensor tilt on the defect signal. Three layer Aluminum sample, each layer of 1 mm thickness, with rivets and 3rd layer sub-surface defect was modeled. Two radial defects of 3mm length and 0.1mm width and two different depths of 20%, and 30% wall thickness were modeled with simulation frequency of 2kHz. The sensor was moved in a linear scan across the rivet and defect and the GMR signals measuring the normal and tangential components were generated. In order to separate the effect of sensor tilt and defect, four different cases were studied, namely, i) no crack ; no sensor-tilt, ii) no crack ; with sensor-tilt, iii) crack; no sensortilt and iv) crack ; with sensor-tilt. The tilt parameter was varied from 00 to 50 for two different defects.

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G. Yang et al. / Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection

The Figure 3 shows the geometry of sensor tilt, where the sensor measures both normal and tangential components in contrast to measuring only normal component when there is no tilt. Hence, if two components of the magnetic field were measured, the magnitude of the tangential component will contain information about sensor tilt and the normal component will contain defect information. Both components of the magnetic fields were measured and studied. The signals ( Bz and Bx components) due 0

to 20% depth subsurface defect with 1 sensor-tilt are shown in Figure 4. The real part of Bx component is seen to be sensitive to defect but insensitive to sensor tilt, whereas the imaginary part of Bz component is seen to be more sensitive to sensor tilt. This offers the potential of detecting defects in the presence of sensor tilt using two component signals.

Figure 3. Field measurement with tilted GMR sensor.

2.2 Feature Analysis and Crack Detection As presented in the Figure 4, the real part of Bx component and imaginary part of

Bz component carry discriminatory information about presence of defect and sensor tilt. In particular, the peak magnitude and slope of peak to peak variation of these signal components have been selected as useful features for classification. The peak magnitude of real part of Bx component is extracted as feature F1 and the slope of peak to peak variation of imaginary part of Bz component represents feature F2. These features are illustrated in Figure 5. The two defined features were calculated from the two defect signals with 10 sensor tilt shown in Figure 4. The features are plotted in the feature space in Figure 6. It is seen that the 4 cases considered ((i) no crack ; no sensortilt, ii) no crack ; with sensor-tilt, iii) crack; no sensor-tilt and iv) crack ; with sensortilt ) are clearly separated in the feature space. Similarly the signals from the two defects (depth 20%) and (depth 30%) with 30 sensor tilt were calculated using the simulation model. The features from these signals are calculated and plotted in Figure 7. It is seen that as the sensor tilt increases, the 4 cases described in section 2.1 are still distinguishable but the separation is lesser that what seen in Figure 6.

G. Yang et al. / Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection

Figure 4. Field measured by the tilted GMR sensor: B z and B x components.

Figure 5. The extracted features based on Bz and B x components.

Figure 6. Features derived from signals in Figure 4 plotted in the two dimensional feature space.

19

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G. Yang et al. / Modeling and Signal Processing Sensor Tilt in Eddy Current-GMR Inspection

Figure 7. Features derived from simulated signals with 3 0 sensor tilt , plotted in the two dimensional feature space.

3. Conclusion An efficient finite element model using reduced magnetic vector potential formulation is presented. The model was validated and used for studying the effect of varying degrees of sensor tilt on EC-GMR signals. Features in GMR output signals were extracted and their ability to distinguish defect signals from sensor-tilt signals were demonstrated for two different tilt angle values. More extensive validation of the approach on experimental signals is under way. A more powerful approach involving invariance transformation using independent component analysis (ICA) is also being investigated for transforming the measured signal so that the transformed signal is invariant to sensor tilt. A sensor system measuring two components of the magnetic field will be built to for experimental validation of the approach.

References [1] Aging of U.S. Air Force Aircraft, National Research Council Final Report, Publication NMAB 488 2, National Academy Press, Washington, D.C., 1997 [2] N. V. Nair, V. R. Melapudi, H. R. Jiminez, X. Liu, Y. Deng, Z. Zeng, L. Udpa, T. J. Moran, and S. S. Udpa, "A GMR based eddy current system for NDE of aircraft structures," IEEE Transactions on Magnetics, vol. 42, no. 10, 2006, pp. 3312 3314 [3] J. C. Aldrin, J. S. Knopp, "Method for crack characterization with noise invariance for eddy current inspection of fastener sites, " Review of Progress in Quantitative Nondestructive Evaluation, vol. 25, 2006, pp. 315 322 [4] X. Liu, Y. Deng, Z. Zeng, L. Udpa, and J. S. Knopp, "Model based inversion technique of GMR signal using element free Galerkin method," Proceedings of the Annual Review of Progress in Applied Computational Electromagnetics, 2008, pp. 221 226

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[5] Z. Zeng, X. Liu, Y. Deng, and L. Udpa, "Reduced magnetic vector potential and electric scalar potential formulation for eddy current modeling," Przeglad Elektrotechniczny, vol. 83, no. 6, 2007, pp. 35 37 [6] Z. Zeng, L. Udpa, S. S. Udpa, and M. S. C. Chan, "Reduced magnetic vector potential formulation in the finite element analysis of eddy current nondestructive testing," IEEE Transactions on Magnetics, vol. 45, no. 3, 2009, pp. 964 967

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-22

Non-Iterative MUSIC-Type Algorithm for Eddy-Current Nondestructive Evaluation of Metal Plates Tommy HENRIKSSON a , Marc LAMBERT a and Dominique LESSELIER a,1 a Département de recherche en électromagnétisme, Laboratoire des signaux et systèmes (CNRS - SUPELEC - Univ Paris-Sud), 3, rue Joliot-Curie, 91192 Gif-sur-Yvette cedex, France Abstract. A non iterative MUSIC type imaging algorithm for time harmonic eddy current testing of a damaged conductive plate is considered. The method is based (i) on a first order asymptotic formulation of the secondary magnetic field observed outside the plate and induced by volumetric defects within it, which is valid when those are small enough with respect to the skin depth at the frequency of operation, and (ii) on the singular value decomposition of the multistatic response matrix that can be collected using an appropriate source and sensor array. Herein, the asymptotic field formulation is validated by comparing the results with those provided by means of the CIVA platform in a realistic case. Further, the singular value pattern and MUSIC images are investigated, for a small spherical void placed at different locations inside a plate. A Gaussian distributed noise is added to the asymptotic data during the initial investigation, to alleviate inverse crime at least in part (more complex arrangements of source/sensor arrays and defects will be considered with external data in a later stage). Yet, these preliminary results as ex hibited indicate the potential of the method to locate small defects in conductive materials in a typical eddy current testing configuration Keywords. Eddy current testing, non iterative inversion, MUSIC type algorithm, Detection of small defects

Introduction Eddy-Current (EC) Non-Destructive Testing (NDT) of metal plates is of interest in a wide range of applications such as quality control in production lines or in-service inspection of industrial facilities. Both tube and plate configurations have been studied earlier, by using different iterative optimization processes [1,2]. Yet, these solutions are computation-heavy and time-consuming, and in many practical situations the processing time certainly is a critical criterion, thus a quicker non-iterative method might be more appropriate, even at the loss of some accuracy in the mapping of the anomalies within the tested workpieces. So, an alternative method could be to solve the inverse problem 1 Corresponding

Author: Département de recherche en électromagnétisme, Laboratoire des signaux et systèmes (CNRS SUPELEC Univ Paris Sud), 3 rue Joliot Curie, 91192 Gif sur Yvette cedex, France; E mail: [email protected]

T. Henriksson et al. / Non-Iterative MUSIC-Type Algorithm

23

by interpolation within an off-line database as is discussed in [3]. Indeed, in general, only the position, and a gross shape of the defect (with the useful distinction between volumetric and crack-like defects also) is of real relevance to EC-NDT. In this case a linearized non-iterative method could be suitable, since implemented with a quasi-real-time functionality, provided that it yields satisfactory results upon position, in particular. In the present study a non-iterative MUSIC (MUltiple SIgnal Classification)-type imaging algorithm is investigated for the detection of small void defects inside a conducting plate. The method has been presented theoretically in the general case of dielectric and/or magnetic volumetric inclusions in free space and full three-dimensional Maxwell’s equations in [4], and it has in particular been successfully developed for the detection of one or several small defects within a dielectric (and possibly lossy) halfspace, in the MHz region [5]. However, to the knowledge of the authors this is the first time that the technique is employed in the low-frequency region (kHz) for EC-NDT, here to image small voids inside a conducting plate. The paper is organized as follows. The setup with the bobbin array, the conducting plate and the void defect is described in section 1. In section 2 the formulation is given for this particular case. In section 3 preliminary results are shown under the form of validation of the asymptotic formulation of the secondary magnetic field by comparing it with the results provided by the simulation tools of the CIVA platform [6], and MUSIC images for a defect at different positions are given for illustration. Some conclusions and perspectives follow.

1. Source-sensor arrangement For illustration of the feasibility of a MUSIC-type algorithm in the EC domain, a compact bobbin array is considered in free space (region 1, ε1 = ε0 ), and operated at a frequency of 100 kHz, as is sketched in Figure 1. It is placed parallel with and above a conducting plate (region 2, Inconel 600, σ2 = 1.02 × 106 S m−1 ), wherein the skin-depth is δs = 1.58 mm at 100 kHz. To simplify, the plate is assumed non-magnetic (μ2 = μ0 ) and linear isotropic with complex permittivity ε2 = ε0 + iσω2 as the time-dependency e−iωt is considered —in practice, the dielectric permittivity can be neglected. Also, in the present study, the plate is considered thick enough to be seen as a half-space. The bobbin array as chosen consists of 7 × 7 transmitting/receiving small coils with inner and outer radii bn = δs /8 (≈ 0.20 mm), cn = δs /6.5 (≈ 0.25 mm), respectively, and a height H = 0.1 mm. The separation between each coil is δs /2 (≈ 0.8 mm) along both the x- and y-axis, and the lift-off of the array is 0.1 mm. During inspection each coil n is transmitting one at the time while all coils including the n one are acting as sensors. The defect within the metal is taken as a small spherical void (εj = ε0 ) with a diameter of aj = δs /10 (0.16 mm) and we consider that it is a priori located inside a 21 × 21 × 21 cell cubic search domain of δs × δs × δs extending right under the centre of the bobbin array. All dimensions of coils and defect are small with respect to the skin-depth δs . Within this constraint the bobbin array can be suitably approximated as an array of magnetic dipoles. Then, the impedance variation due to the defect is equivalent to the variation of (n) the z-polarized magnetic field Hs (r) · ˆ z at the center of the coil located at r (again it might be the centre of the emitting coil as well as the centre of all other non-emitting

24

T. Henriksson et al. / Non-Iterative MUSIC-Type Algorithm

Figure 1. The arrangement for the eddy current MUSIC type algorithm investigation is sketched: a 7 × 7 (or 3 × 5 inside the dark rectangle) bobbin array above a non magnetic conducting plate affected by a small spherical defect (with radius aj ) inside the search domain somewhere under the array. (n)

coils). Similarly, the primary electric field E0 (xj ) inside the search region may be computed by using the appropriate dyadic Green’s function Gem t (xj , r) of the configuration. The small size of the defect keeps the asymptotic formulation of the secondary magnetic field valid, as is seen next. Otherwise, it could be argued that the overall dimensions of the array are not that large (side of 3δs ); yet number and location of coils as hypothesized remain realistic in view of the technology whilst most of the anomalous field due to the assumed defect under it appears to be collected (in practice also an array will be moved step by step in either direction to cover a wider zone).

2. Mathematical formulation The MUSIC algorithm herein is based upon a first-order asymptotic formulation of the secondary magnetic field outside the plate induced by volumetric defects within it, which is valid when those are small enough with respect to the skin-depth at the frequency of operation, and on the Singular Value Decomposition (SVD) of the so-called Multistatic Response (MSR) matrix collected using, e.g., the bobbin array.The method is briefly described below for the particular case of ECT. A detailed description of the MUSIC algorithm in the small-defect framework for the full Maxwell’s equations is found for the general case in [4], with [5] as an illustration in a stratified-space case similar with ours save made in the propagative (microwave) regime —here only diffusion occurs. 2.1. Asymptotic formula — secondary magnetic field Considering P small spherical voids centered at xj and with radii aj  δs , the asymp(n) totic formulation of the secondary magnetic field Hs (r) may be formed as

25

T. Henriksson et al. / Non-Iterative MUSIC-Type Algorithm

Hs(n) (r)

=H

(n)

(n) (r) − H0 (r)

=−

P  

iω2 Gme r (r, xj )

· Mj

j=1

j , Vj 2





·

(n) E0 (xj )

,

(1) where n is the transmitter index (centered at rn ). Letting I be the identity tensor, the polarization tensor Mj for such void spherical defects (j = 0 ) is given by

Mj

j , Vj 2

 =

4πa3j 3(j − 2 ) . |Vj |I, where |Vj | = 22 + j 3

(2)

The Gme r (r, xj ) term is the dyadic Green’s function between the defect and the receiving bobbin array; it satisfies the following differential equation 2 me ∇ × ∇ × Gme r (r, xj ) − k Gr (r, xj ) = ∇ × Iδ(r − xj ),

(3)

considering the defect as an electric impulse current, with usual magnetic-type boundary conditions, k free-space (air) wavenumber. Since the radius of each bobbin array element is bn  δs the dyadic Green’s functh tion Gem t (xj , rn ) between the n transmitting coil of the array placed at rn and the (n) defect can be used to compute the primary magnetic field E0 (xj ) as (n)

E0 (xj ) = Gem z, t (xj , rn ) · ˆ

(4)

where the differential equation satisfied for a magnetic impulse current source is 2 em ∇ × ∇ × Gem t (xj , rn ) − k Gt (xj , rn ) = ∇ × Iδ(xj − rn ),

(5)

with usual electric-type boundary conditions. 2.2. MUSIC imaging From the secondary magnetic field the Multistatic Response matrix A is given as A=

P 

em G me r (xj ) · Mj · G t (xj ),

(6)

j=1 em where the matrices G me r (xj ), a M × 3 matrix, and G t (xj ), a 3 × N matrix, are constructed from the dyadic Green’s functions as

⎧ me z, . . . , Gme z ]t , ⎨ G r (xj ) = k 2 [Gme r (r1 , xj ) · ˆ r (rM , xj ) · ˆ ⎩

em 2 G em z, . . . , Gem z]t . t (xj , rN ) · ˆ t (xj ) = k [Gt (xj , r1 ) · ˆ

(7)

M and N are the numbers of receiving and transmitting array elements, respectively (they are not necessarily equal), t denoting the transpose. Since the MSR matrix has the dimension N × M is it possible to apply the Singular Value Decomposition (SVD)

26

T. Henriksson et al. / Non-Iterative MUSIC-Type Algorithm

A = UΣV∗ ,

(8)

where ∗ denotes transpose conjugation. The number of nonzero singular values s in Σ, em for the j th defect, depends upon the rank of the matrices G me r (xj ) and G t (xj ). In our case, to each defect, will correspond only two singular values —since only magnetic fields are collected, referring to [4] for further mathematical analysis— as numerically illustrated later on in section 3.2. By the first s columns of U and V (Us , Vs ) the orthogonal projection onto the left and right signal space can be defined as Pr = (I − Us U∗s ),

(9)

Pt = (I − Vs Vs∗ ).

(10)

When M = N , the imaging function W(x) is given by W(x) =

1 ||Pr (G me r (x)

·

a)||2

+

1 ||Pt (G em t (x)

· a)||2

,

(11)

where a = (1, 1, 1) [4]. Other values of a could be considered, taking different field components into account, how to achieve the best choice of a needing further analysis.

3. Results The results presented next validate the framework of analysis considering only one spherical void inside the plate in account with the material shown in section 1. 3.1. Numerical Validation - CIVA The asymptotic formulation of the secondary magnetic field is validated by comparing the results with those achieved via modeling tools of the CIVA platform [6]. The impedance variations due to a defect of volume Vj are obtained by a proper calculation of the volume integral ΔZnm = −

1 In Im

 Vj

(m)

(n)

E0 (r) · Jj (r)dr,

(12)

letting In and Im the currents in the emitting coil n and the receiving coil m (consid(m) ered as a fictitious emitter), E0 (r) the primary field due to the coil m and Jj (r) the volumetric eddy-current in Vj due to the source n [2]. Since the radius of the bobbin element bn  δs , the z-polarized magnetic field from the asymptotic formulation should  (n) be equivalent to the CIVA-computed impedance variation, Hs (rm ) · ˆ z ≈ ΔZnm . To verify this, a smaller 3 × 5 bobbin array (depicted in Figure 1) is used with the void (a = δs /10) at the centre of the search region (δs /2 depth). The spherical void is modeled as a cube discretized by 5 × 5 × 5 cells in the CIVA model, which gives a RMS error less than 0.2% on the computed results, compared to using a higher number of cells.

T. Henriksson et al. / Non-Iterative MUSIC-Type Algorithm

27

The comparison in magnitude between the z-polarized magnetic field from the asymptotic formulation and the impedance variation from CIVA is illustrated in Figure 2, 6 different coils in the bobbin array transmitting (specified as bobbin 1 − 3 and 8 − 10 in Figure 1). The asymptotic results (♦) fit very well with the CIVA results (—) in all cases except when the transmitting coil is right over the void (Figure 2 (d)). In this case indeed, (8) the primary field E0 (x1 ) is very small at the center of the defect. Since the asymptotic formulations are only using this central value, the result is quite different from the one yielded by carrying out the volume integral. However, except this peculiar point, it appears that the asymptotic formulation and the more brute-force approach via a CIVA tool provide very close results. 3.2. Construction of the images - MUSIC Once the asymptotic formulation has been validated, it can thus be used to compute the MSR matrix A for the 7 × 7 bobbin array. To minimize the inverse crime a Gaussian distributed complex noise is added onto the data (SNR = 10 dB) as Anoise = A + σθ,

(13)

where θ is a M ×N matrix filled with normal distributed pseudorandom complex values, with an average of zero, and the variance σ defined as    |A|2  − 10  10 log10 MN . σ= 2

(14)

The same void is to be retrieved at two different depths (δs /4 and 3δs /4). In Figure 3 both the singular value distribution and the MUSIC image are depicted, for both positions. As expected, the void is associated with two nonzero singular values (much larger than all others, which should ideally be zero, and for all what matters very small compared to the two main ones), where the amplitudes are decreasing with the depth of the defect. However in this investigation the SNR of the data has been kept constant between both positions, which might not be so realistic. The MUSIC images are iso-surface plots of W(x) with an iso-level of 70%. The position of the void appears well retrieved for both locations inside the search region, which is also the case (examples not shown) everywhere inside the search region. However, with increasing depth the reconstruction along the z-axis gets more blurred (less powerful signal is acquired, and the aperture angle under which the defect is seen is getting smaller and smaller).

4. Conclusion and future work A non-iterative MUSIC-type imaging algorithm has been introduced in the framework of EC-NDT of a conductive plate. The asymptotic field formulation on which it is based has been validated by comparing asymptotic results with those provided by simulation tools of the CIVA platform where the interaction is simulated from a full field integral

28

T. Henriksson et al. / Non-Iterative MUSIC-Type Algorithm

1

x 10

4

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

2

4

6

8

10

12

14

0

x 10

4

2

4

6

(a)

1

x 10

4

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

2

4

6

8

10

12

14

0

x 10

x 10

4

1

0.8

0.6

0.6

0.4

0.4

0.2

0.2

2

4

6

8

(e)

12

14

2

4

6

8

10

12

14

10

12

14

(d)

0.8

0

10

4

(c)

1

8

(b)

10

12

14

0

x 10

2

4

4

6

8

(f)

Figure 2. Comparison in magnitude between the variation of impedance computed via CIVA ( ) and the (♦), z polarized magnetic field from the asymptotic formulation with a computed primary field E0 using Gem t along the 15 (3 × 5) receiving coils when transmitting from (a) coil 1, (b) coil 2, (c) coil 3, (d) coil 8, (e) coil 9, (f) coil 10.

formulation using a method of moments. Preliminary results for a single small spherical void have been presented, as illustration of the good potential of the method. The position of the void is indeed successfully retrieved along all three axes, with high accuracy even in presence of strong noise, whatever its location within the plate. Future work should involve more complex arrangements of the bobbin array and several small defects, and also multi-frequency data. The inverse crime should be further minimized by constructing the MSR matrix from CIVA data. More complex defects

T. Henriksson et al. / Non-Iterative MUSIC-Type Algorithm

29

Figure 3. Singular value distribution and images for two positions of the void (a δs /10), with the 7 × 7 bobbin array setup. (left) at (−0.3, 0, −0.3)δs and (right) at (0.3, 0.3, 0.3)δs . The exact voids are displayed as transparent spheres as well.

should be investigated in order to see whether their size can be approached to an extent via a determination of their polarization tensor, main emphasis being however on the investigation of crack-like defects, for which the theoretical machinery might still be incomplete (which does not preclude useful numerical experimentation).

References [1] [2] [3] [4] [5] [6]

D. Dos Reis, M. Lambert, and D. Lesselier. Eddy current evaluation of three dimensional defects in a metal plate. Inverse Problems, 18:1857 1871, 2002. J. F. P. J. Abascal, M. Lambert, D. Lesselier, and O. Dorn. 3 D eddy current imaging of metal tubes by gradient based, controlled evolution of level sets. IEEE Trans. Magn., 44:4721 4729, 2008. S. Bilicz, M. Lambert, and S. Gyimóthy. Kriging based generation of optimal databases as forward and inverse surrogate models. Inverse Problems, 26(7):074012, July 2010. H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson. Music type electromagnetic imaging of a collection of small three dimensional inclusions. SIAM J. Sci. Comput., 29:674 709, 2007. S. Gdoura, D. Lesselier, P. C. Chaumet, and G. Perrusson. Imaging of a small dielectic sphere buried in a half space. ESAIM:Proceedings, 26:123 134, 2009. CIVA: State of the art simulation platform for NDE. http://www civa.cea.fr.

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-30

Identification of Defects in 3D Space Using Computer Radiography System Wojciech CHLEWICKI1, Piotr BANIUKIEWICZ, Tomasz CHADY and Andrzej BRYKALSKI Department of Electrical and Computer Engineering, Faculty of Electrical Engineering, West Pomeranian University of Technology, al. Piastow 17, 70-310 Szczecin, Poland

Abstract. A radiographic system for identification of defects in three-dimensional space has been built and tested. It is a cost effective alternative to sophisticated fully three-dimensional tomography systems. We present initial results of using the extended radiographic system for the images of the phantom made of wood and pieces of copper. Keywords. Radiography, computed tomography

Introduction Fully three-dimensional tomographic X-ray inspection of an object requires projections to be taken around 360 degrees. This is not possible in many circumstances due to time and accessibility restrictions and can only be obtained using sophisticated computed tomography (CT) systems. A much simpler (and cheaper) way for doing radiographic inspection is using digital radiography systems. However, the output of digital radiography is a two dimensional image which is a projection of three-dimensional objects. In nondestructive testing this could be a strong limitation. Firstly, the information about the depth is lost. Secondly, the defects at different depth may overlap, i.e. they may appear as one defect in the radiographic projection. Thirdly, planar defects can be positioned parallel to irradiating X-rays and hence would not be detected in the image. Lastly, there are strong requirements on maximal time of acquisition and reconstruction, which limits the use of CT systems. In this paper we present initial results of using the extended radiographic system for identification of defects in three-dimensional space. The system is a cost effective alternative to sophisticated fully three-dimensional tomography systems. The initial results of recovering the position in three dimensions are presented. The abilities and limitations of the system are discussed.

1

Corresponding author. E-mail address: [email protected]

W. Chlewicki et al. / Identification of Defects in 3D Space Using Computer Radiography System

31

1. System description 1.1. Image acquisition Projection data have been acquired using the system presented in Figure 1. The system consists of a X-ray source CP1201, a digital detector Shad-o-Box™1024, a manual positioning system, a frame grabber and a PC workstation. In the near future the manual positioning system will be replaced with motorized one. The acquisition of radiographic projections has been performed along a linear trajectory. The X-ray source is moved above the object whose position is fixed in space. Such an image acquisition scheme is an equivalent to limited angle tomography which was shown by Zhou et al. [1] and confirmed by Gondrom et al. [2]. Their systems, however, are characterized by a linear translation of the object instead of a motion of the detector like in our system. 1.2. Image reconstruction Approximate three-dimensional image reconstruction from projections has been carried out using iterative algorithms. An adaptation of Algebraic Reconstruction Techniques (ART) [3] has been implemented in order to perform reconstruction from projections. It takes into account the linear source detector trajectory. ART is an iterative-type image reconstruction algorithm that has been proven superior to the widely used Filtered Backprojection algorithm in case of limited angle tomography [4]. The ART algorithm consists of a series of successive projections and backprojections (of the correction) of the reconstructed image. Each step within the algorithm is detailed in the scheme depicted in Figure 2. As a result, we obtained a volume which possibly fits all acquired X-ray projections. The correction formula of ART is presented below N

v(jk +1) = v (jk ) + λ

pi − ¦ winvn( k ) n =1 N

¦w

wij

2 in

n =1

(1)

where vj is a reconstructed volume element, pi is a projection element, win is an element of the system matrix and Ȝ is a relaxation coefficient. The algorithm has been implemented in 64-bit Visual C++. The three-dimensional projection mechanism is using tri-linear interpolation. The size of the reconstructed volume has been set to 1024x1024x1024. Our experiments showed that the number of 2 iterations is sufficient.

32

W. Chlewicki et al. / Identification of Defects in 3D Space Using Computer Radiography System

Figure 1. The radiographic system.

Figure 2. Iteration scheme of the image reconstruction algorithm.

1.3. Depth identification The root mean square (RMS) contrast has been used to calculate the contrast of the Region of Interest (ROI) containing the inclusion for all slices. It is defined as the standard deviation of the pixel intensities. Maximum of the Crms stands for the inclusion being in focus:

W. Chlewicki et al. / Identification of Defects in 3D Space Using Computer Radiography System

C RMS =

1 MN

N −1 M −1

¦ ¦ ( ∇ I (i , j ) − ∇ I (i , j ) )

2

33

(2)

i=0 j =0

where: Crms is the root mean square contrast function, M and N stand for width and height of the ROI respectively and I is a map of pixel's intensity of the ROI. The RMS contrast does not depend upon the spatial frequency content or the spatial distribution of contrast in the image.

2. Experiments 2.1. Phantom The phantom is made of wood as a three-slice structure, two inclusions of copper representing the defects (material, inhomogenity). Copper was put inside holes drilled in two wooden slices. Dimensions of the phantom are 50 mm x 50mm x 50 mm. 2.2. Data acquisition Seven projections of size (1024x1024) have been acquired in the manner described in the above. The voltage of the X-ray tube has been set to 80kV, the current being equated to 1 mA. The integration time of the detector has been set to 4s. During the acquisition process the source is moved along the linear trajectory, the range of linear translation of the detector and the object being (-28cm, 28cm). In such a way, 7 radiographic projections have been taken at different source positions. 2.3. Results of reconstruction The acquired projection has been input for the reconstruction of the 1024x1024x1024 volume. Some of the significant slices for depth identification are displayed in Figure 3. Left hand side inclusion is in focus in slice number 271 whereas in the other crossections it appears blurred. The right hand inclusion is "in focus" in slice number 146. This proves the abilities of the system to localize the depth of the occurrence of certain objects within the investigated volume. In Figure 4 the process of depth identification is visually presented.

Figure 3. Crossections of number 101, 121, 146, 201, 271 and 406 (from left to right) within the reconstructed volume. The maximum of sharpness for each inclusion is clearly visible making it possible to localize the depth of each inclusion.

34

W. Chlewicki et al. / Identification of Defects in 3D Space Using Computer Radiography System

Figure 4. Results of depth identification.

3. Conclusions The ability of the system to localize the depth of the occurrence of objects within the investigated volume has been experimentally confirmed. It can be concluded that the diagnostic value of digital radiography systems could be significantly improved via only minor extensions of the systems themselves. Further work is required in order to assess the impact of changes of the linear translation range on the quality of the pseudo reconstructed volume [5].

Acknowledgments The work was conducted in the framework of the research project “Identification of structural heterogeneities in mechanical systems”, supported by the Polish Ministry of Science and Higher Education. Grant no. 1141/B/T02/2009/36 (2009-2012).

W. Chlewicki et al. / Identification of Defects in 3D Space Using Computer Radiography System

35

References [1] J. Zhou, M. Maisl, H. Reiter, W. Arnold, Computed laminography for material testing. Appl. Phys. Lett. 68, 3500. [2] Gondrom S., Zhou J., Maisl M., Reiter H., Kroning M., Arnold W.: X-ray computed laminography approach of computed tomography for applications with limited access. Nuclear Engineering and Design 190, 1999, pp. 141-147. [3] Kak A., Slaney M.: Principles of Computerized Tomographic Imaging. Philadelphia: SIAM, 2001. [4] A. H. Andersen, “Algebraic Reconstruction in CT from Limited Views,” IEEE Trans. Med. Img., vol. 8, no.1, 1989, pp. 50-55. [5] B. Li, G. B. Avinash, R. Uppaluri, J. W. Eberhard, B.E.H. Claus, The impact of acquisition angular range on the z-resolution of *radiographic tomosynthesis, International Congres Series 1268, 2004, pp. 13-18.

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-36

A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole S. K. BURKE 1 Defence Science and Technology Organisation, Melbourne, Australia

Abstract. Eddy-current induction by a coaxial circular air-cored coil in a cracked borehole is considered in the limit of small electromagnetic skin depth. A closed form expression is derived for the change in coil impedance ΔZ due to a long axial crack with constant depth and opening based on an extension of the Lewis extended surface impedance boundary conditions to a cylindrical geometry. The theoretical predictions are compared with experimental measurement of ΔZ for a series of boreholes containing wire-cut slots in 2024 Al alloy test specimens. The model predictions were in good agreement with experiment for smaller slot depths, with the accuracy tending to decrease as the slot depth increased. In all cases, the predictions were superior to those based on a simple Born approximation. Keywords. Eddy-current NDE, thin-skin theory, bolthole cracks

Introduction Fastener holes in aircraft act as stress concentrators and are common sites for fatigue cracking. If left undetected, the growth of such fatigue cracks can lead to catastrophic structural failure. Considerable effort has been devoted to the development of nondestructive evaluation (NDE) techniques which can detect cracks in fastener holes with high reliability. Along with ultrasonic testing, eddy-current NDE is foremost among these techniques. The theory underpinning eddy-current NDE for cracks in cylindrical geometries such as fastener holes continues to be developed, including recent approaches based on boundary element methods [1]. However, unlike planar geometries, for which there are highly effective analytical approximations valid in the limit of small electromagnetic skin depth [2-4], there are currently no similar highly developed thin-skin models for cylindrical geometries which can be used to complement finite-element and boundary element methods. In this paper, a thin-skin model for eddy-current NDE of cracks in a fastener hole is presented based on an extension of the Lewis extended surface impedance boundary conditions [4] to a cylindrical geometry. In Section 1, a closed-form expression for the change in coil impedance ΔZ is presented for the simple case of a coaxial bobbin coil in a borehole containing a long crack with uniform depth and opening. The coil is assumed to be sufficiently remote from the ends of the hole that the hole can be treated

1

Corresponding Author. S K Burke, Maritime Platforms Division, DSTO, 506 Lorimer St., Fishermans Bend, Vic 3207 Australia. Email: [email protected]

37

S.K. Burke / A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole

as a “borehole”, i.e. infinite in length. The theoretical predictions are compared with experimental results in Sections 2–3 and the significance of the work is discussed.

1. Theory The configuration is shown schematically in Fig. 1 where a cylindrical air-cored coil carrying an alternating current I exp(iω t) is centred coaxially in a borehole containing a longitudinal crack. The coil, of length 2h, is wound with N turns and has inner and outer radii r1 and r2 respectively. The borehole has a radius a and the length of the hole is assumed to be infinite. The crack has a uniform depth b, uniform opening Δu and is infinite in length. The line of the crack is parallel to the z-axis at θ = 0 with the crack faces in the xz-plane. The parent metal is assumed to have an isotropic electrical conductivity σ and linear magnetic permeability μ =μrμ0 where μr is the relative permeability and μ0 is the permeability of free space. As usual in eddy-current NDE, the frequency is assumed to be sufficiently low that the quasistatic approximation can be used. In the following, the problem is formulated in terms of current-free regions using the magnetic scalar potential ϕ where the magnetic field is related to ϕ via H = ∇ϕ

(1)

and ϕ satisfies the three-dimensional Laplace equation

∇ 2ϕ = 0.

(2)

In the limit of small skin depth ( δ = [2/(ωσμ)]½ ) the normal component Hn of the freespace magnetic field at the surface of an uncracked conductor satisfies the surface impedance boundary condition [6]

x

y

Figure 1. Eddy-current induction by a coaxial source coil in a borehole containing a long rectangular slot.

38

S.K. Burke / A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole

∂H n = (γ − ∇ ⋅ n) H n ∂n

(3)

where n is the outward normal to the conductor surface and γ = (1+i)/(μrδ). From Eqs.(1) and (3) the surface impedance boundary condition for an uncracked borehole using the coordinate system shown in Fig.1 is

∂ 2ϕ 1 ∂ϕ = −(γ + ) , r = a. 2 ∂r r ∂r

(4)

Clearly Eq.(4) is not valid in the presence of a crack and must be modified. By considering the flux leaving the mouth of the crack, Lewis [4] derived an “extended” surface impedance boundary condition for a planar conductor containing a crack. Extending this approach to cylindrical geometries, the extended surface impedance boundary condition for the cracked borehole in Fig.1 can be written as, ∂ 2ϕ ( e ) 1 ∂ϕ ( e ) 2 γ + ( + ) = − H n( i ) δ (θ ), r = a, r ∂r a ∂r 2

(5)

and links the fields within the crack (the interior fields, denoted by the superscript i) and the fields within the borehole (the exterior fields – denoted by the superscript e). In deriving Eq.(5), and in the following sections, it is initially assumed that the crack has zero opening. The effect of crack opening is introduced in Section 1.4. 1.1. Exterior fields – fields within the borehole The exterior scalar potential can be regarded as the superposition

ϕ ( e ) = ϕ ( s ) + ϕ ( r ) , a ≤ r ≤ r2 ,

(6)

of the known source potential ϕ (s) of the isolated coil in free space [7] and the potential ϕ (r) arising from induced currents in the cracked conductor. A representation for the potential ϕ (r) can be constructed by solving Eq.(2) in cylindrical coordinates using the method of separation of variables. If the origin of the polar coordinate system is chosen to lie at the center of the coil, then

ϕ ( r ) (r ,θ , z ) =

2

π³

∞ 0

sin(λ z ) ϕˆ ( r ) (r , θ ; λ ) d λ , r ≥ a,

(7)

∞

ϕˆ ( r ) (r ,θ ; λ ) = c0 I 0 (λ r ) + 2¦ cn I n (λ r ) cos(nθ ),

(8)

n =1

where In are modified Bessel functions and the carat denotes the Fourier sine transform

39

S.K. Burke / A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole ∞ fˆ (r ,θ ; λ ) = ³ sin(λ z ) f (r ,θ , z ) dz .

(9)

0

Note also that ϕ (r) is an odd function of z and an even function of θ . The unknown coefficients cn = cn(λ) are to be determined by application of the extended surface impedance boundary condition Eq.(5) once a suitable representation for the potential within the crack has been derived. 1.2. Interior fields – fields within the crack It is convenient to describe the fields within the crack using the Cartesian coordinate system in Fig.1. In the thin-skin limit ϕ (i) satisfies the 2D Laplace equation [4] ∂ 2ϕ (i ) ∂ 2ϕ (i ) + = 0, a ≤ x ≤ a + b. ∂x 2 ∂z 2

(10)

The boundary conditions on ϕ (i) are as follows: •

Continuity condition on the tangential component of H at the crack mouth, ∂ϕ ( i ) ∂ϕ ( e ) = , ∂z ∂z

•

y = 0, x = a.

(11)

Thin-skin boundary condition on Hn at the crack tip [2–3,5], ∂ϕ ( i ) = 0, x = a + b. ∂x

(12)

The solution of the boundary value problem defined by Eqs.(10) – (12) can be solved through the use of Fourier transforms [9]. The resulting Fourier sine transform of the interior potential takes the form

ϕˆ ( i ) ( x; λ ) = ϕˆ ( e ) (a, 0; λ ) cosh[λ (a + b − x)] / cosh(λ b),

a ≤ x ≤ a + b.

(13)

1.3. Solution Closed form solutions for ϕ can now be derived using the representations obtained in sections 1.1–1.2. The extended surface impedance boundary condition Eq.(5) linking the exterior and interior potentials can be written in terms of sine Fourier transforms as −γ a 2

∂ϕˆ ( e ) ∂ 2ϕˆ ( e ) + − λ 2 a 2ϕˆ ( e ) = 2aHˆ n(i ) δ (θ ), r = a, ∂r ∂θ 2

(14)

where the term involving the second derivative with respect to r has been eliminated using Eq.(2). From Eqs. (1), (9) and (13) it follows that

40

S.K. Burke / A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole

Hˆ n( i ) ( x = a; λ ) = λ ϕˆ ( e ) (a, 0; λ ) tanh[λ b].

(15)

Substituting Eqs.(6), (8) and (15) into Eq.(14) and simplifying gives the condition ∞

β s + c0 β 0 + ¦ cn β n cos(nθ ) = n =1

∞

(16)

2λ a tanh(λ b) × [ϕˆ ( s ) + c0 I 0 (λ a) + 2¦ cn β n cos(nθ )]δ (θ ), n =1

where βs, βn and ϕˆ ( s ) are the known functions,

ϕˆ ( s ) (r , 0; λ ) = − nd I sin(λ h) K 0 (λ r ) I (r1 , r2 ), ª ∂ϕˆ ( s ) (r , 0; λ ) º » , ∂r ¬ ¼r =a

β s = −λ 2 a 2ϕˆ ( s ) (a, 0; λ ) − γ a 2 «

(17)

(18)

β n = −λ γ a I n′ (λ a ) − (n + λ a ) I n (λ a). 2

2

2

2

Note that in Eq.(17), nd = N/[2h (r2 – r1)] denotes the coil turn density and I ( r1 , r2 ) = ³

λ r2

λ r1

x I1 ( x) dx.

(19)

It is useful first to consider the solution to Eq.(16) in the absence of the crack b = 0. In this case c0 = –βs/β0 and cn = 0 for n ≠ 0 as the fields are axisymmetric. Hence, from Eqs.(6) and (8), the Fourier sine transform of the scalar potential on the surface of the uncracked borehole in the thin-skin limit is

ϕˆ ( u ) (a, 0; λ ) = ϕˆ ( s ) (a, 0; λ ) − β s I 0 (λ a ) / β 0 .

(20)

It can be shown that the thin skin expression Eq.(20) agrees with the exact expression [7] for an uncracked borehole to order 1/γ as required. In the presence of the crack, Eq.(16) can be solved for the unknown coefficients cn by multiplying both sides of the equation by cos(mθ) where m = 0,1,2 … , integrating over the interval –π ≤ θ ≤ π and applying the cosine orthogonality conditions. Solving the resultant simultaneous equations and using Eq.(20) gives the final coefficients

β s aλ tanh(λ b) + ϕˆ ( u ) (a, 0; λ ), β 0 πβ 0 [1 + tanh(λ b) G (λ )] cn = ( β s + c0 β 0 ) / β n , n ≥ 1, c0 = −

where the function G(λ) is the infinite sum

(21)

S.K. Burke / A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole ∞ aλ ª º ( ) / 2 I λ a β I n (λ a ) / β n » , + ¦ 0 0 « π ¬ n =1 ¼ ∞ ξ 1 , = ¦ π n =−∞ q ξ I n′ (ξ ) / I n (ξ ) + n 2 + ξ 2

41

G=−

(22)

and the arguments q = γ a and ξ = λ a are dimensionless. Evaluation of the slowly convergent infinite sum G can be performed efficiently for small or large arguments using asymptotic expansions and, for more general arguments, by subtracting out the known series for digamma functions and summing the more rapidly convergent difference numerically. In the limit of large a it can be shown that Eq.(22) reduces to the expression derived by Lewis [4] for the planar case. Substituting Eq.(21) into Eqs.(6)–(8), and making use of Eq.(20), gives the following closed-form expression for the sine Fourier transform of the magnetic scalar potential at the mouth of the crack,

ϕˆ ( e ) (a, 0; λ ) = ϕˆ ( u ) (a, 0; λ ) [1 −

tanh(λ b) G (λ ) ]. 1 + tanh(λ b) G (λ )

(23)

Combining Eq.(1) and Eq.(23) and using the properties of the Fourier transform, the tangential component of magnetic field at the mouth of the crack can be written H z ( a, 0, z ) = H z( u ) (a, 0, z ) −

2

π³

∞ 0

λ cos(λ z ) tanh(λ b) G (λ ) (u ) ϕˆ (a, 0; λ ) d λ , 1 + tanh(λ b) G (λ )

(24)

where the first term is the tangential field for an uncracked borehole and the second term is the field scattered by the crack. Note for simple thin-skin models [5] the scattering term in Eq.(24) is omitted: an approach termed “the Born approximation”. 1.4. Coil impedance change due to the crack An expression for ΔZ in the thin-skin limit due to a crack with finite opening Δu can now be obtained using the knowledge of the fields obtained in the proceeding subsections. The derivation closely parallels that in previous work for the related case of an infinitely long rectangular slot in a half-space [2,3,5,9] and relies on the application of surface impedance boundary conditions to the general Auld ΔZ formula [5] for a defect in a conductor. The higher-order “Kahn effect” contributions to ΔZ are also included by assuming that the curved corner fields take the same form [2] as for a 90º edge. Following this approach, it can be shown that I 2 ΔZ =

4ωμ0

π

³

∞ 0

g [ϕˆ ( u ) (a, 0; λ )] 2 d λ , 1 + tanh(λ b) G (λ )

where the coefficients take the form g = i Δu g f + (1 + i) μ r δ ( g f − 12 Δu g 0 ) + 12 μ r δ 2 g k ,

(25)

42

S.K. Burke / A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole

g f = λ tanh(λ b), g 0 = λ 2 [1 − sech(λ b)],

(26)

g k = −4 (1 + λ ) / π + λ sech(λ b). 2

2

2. Experiment

Experiments were performed to test the validity of the theory presented in Section 1. The experiments were carried out using a series of air-cored coils and a set of 10 mm diameter bolthole specimens containing simulated cracks. The coil parameters are given in Table 1. The test specimens were prepared by drilling and reaming a series of through holes in thick 2024 Al alloy plate. The electrical resistivity of the plate was 6.0±0.05 μΩcm and the plate thickness (hole length) was 24.6 mm. The simulated cracks were introduced into the reamed holes by electro-discharge machining a slot using a thin wire electrode. The specimen parameters are given in Table 2. Coil impedance measurements were made over the frequency range 5kHz–400kHz using a low frequency impedance analyser (HP-4192A). The change in coil impedance due to the slot ΔZ was determined by measuring the difference in impedance when the coil is centered in a cracked bolthole and when the coil is centered in an uncracked reference hole with the same diameter. The impedance data were corrected for the effects of stray capacitance using a procedure described previously [8]. Table 1. Coil parameters Inner radius r1 (mm) 3.845

Outer radius r2 (mm) 4.43

Length 2h (mm) 7.805

Turns N 408

Inductance L0 (μH) 809.5

Resonant frequency fR (kHz) 770

Table 2. Slot parameters and designations. The borehole radius a = 5.00 ± 0.005 in an 2024 Al-alloy block Slot BB15 depth b (mm) 1.33 ± 0.02 opening Δu (mm) 0.32

Slot BB13 3.02 ± 0.02 0.30

Slot BB2 4.04 ± 0.02 0.29

Slot BB3 6.01 ± 0.04 0.30

Slot BB5 8.04 ± 0.08 0.31

Slot BB4 10.05 ± 0.05 0.31

3. Results and Discussion

In Fig. 2, the experimental values of ΔZ are compared with the theoretical predictions obtained using Eq. (25). The results are plotted as a function of skin depth (rather than frequency) to illustrate the structure of the data clearly. Also shown in Fig. 2 are the predictions of the Born approximation, for which the scattering term in Eq.(25) is neglected by setting G(λ)=0. As shown in Fig.2a, the calculated values of the coil inductance change ΔL are in good agreement with experiment for small slot depths (b ≤ 6 mm ) but less so for larger depths where the scattering from the crack is greater. Nevertheless, even for these deeper slots (up to b = 10 mm examined here), good agreement is obtained at the smallest skin depths within the range. In all cases, the model predictions are superior to those of the Born approximation for which the scattering is neglected entirely.

43

S.K. Burke / A Thin-Skin Model for Eddy-Current NDE of Cracks in a Borehole 12

45

Experiment Calculated Born

b=10 mm 10

35

Resistance Change (Ω)

Inductance Change (μH)

40

30 b (mm) 25 10 20 15 10 5 0 0.0

8 6 4

Experiment Calculated Born

8 4 mm 6 4 1.3 mm 2

(b)

(a)

3 1.3 0.2

0 0.4 0.6 0.8 1.0 Skin Depth (mm)

1.2

1.4

0.0

0.2

0.4

0.6 0.8 1.0 Skin Depth (mm)

1.2

1.4

Figure 2. Change in (a) coil inductance and (b) coil resistance due to the slot as a function of skin depth.

The corresponding results for the coil resistance change are shown in Fig.2b. The agreement between the model predictions and experiment is good for all slots at small skin depth but becomes markedly poorer with increasing skin depth. This is likely due to the assumption in Eq.(25) that the planar “Kahn effect” term (which contributes to ΔR to a greater extent that ΔL) can be adopted for a cylindrical geometry. The model predictions for ΔR overall are again superior to those based on the Born approximation. Although the experiments were performed using Al alloys, the model is applicable to magnetic steels for which μr ≠ 1. Future experimental work on magnetic materials would be valuable, particularly as this provides access to significantly smaller skin depths. The analysis can also be extended to more complex defect types, such as a pair of longitudinal cracks located on opposite sides of the borehole, and to more complex coil configurations, e.g. where the coil axis is normal to the borehole surface. The present model, in which the scattering is incorporated using extended surface impedance boundary conditions, is superior to the Born approximation and represents the most complete thin-skin theory for eddy-current NDE of cracks in boreholes to date. It does not, however, achieve the typical accuracy obtained for planar geometries for which the scattering from the crack has been treated more completely by Harfield and Bowler [2-3]. Further theoretical work is clearly required but the extension of the Harfield-Bowler approach to cylindrical geometries does not appear straightforward.

References [1] [2] [3] [4] [5] [6] [7] [8] [9]

J.R. Bowler and T.P. Theodoulidis, IEEE. Trans. Magn. 45 (2009), 1012–1015. N. Harfield and J.R. Bowler, J.Appl.Phys. 82: (1997), 4590–4603. J. R. Bowler and N. Harfield, IEEE. Trans. Magn. 34 (1998) 515–523. A.M. Lewis, J.Phys.D: Appl. Phys. 25 (1992), 319–26. B.A. Auld and J.C. Moulder, J.Nondestr.Eval. 18 (1999), 3–36. A. Nethe, R. Quast and H. Stahlmann, IEEE.Trans.Magn. 34 (1998), 3331–3334. C.V. Dodd, W.E. Deeds and J. W. Luquire, Int.J.Nondestr.Test. 1 (1969), 233–293. D.J. Harrison, L.D. Jones and S.K. Burke, J.Nondestr.Eval. 15 (1996), 21–34. S.K.Burke, J.Appl.Phys., 76 (1994), 3072–3080.

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-44

Magnetic Response Field of Spherical Defects within Conductive Components M. KREUTZBRUCK and H.-M. THOMAS, R. CASPERSON, V. REIMUND and M. PELKNER BAM Federal Institute for Materials Research and Testing, 12205 Berlin, Germany

Abstract. The determination of magnetic distortion fields caused by inclusions hidden in a conductive matrix using homogeneous current flow needs to be addressed in multiple tasks of electromagnetic non destructive testing and materials science. This includes a series of testing problems such as the detection of tantalum inclusions hidden in niobium plates, metal inclusion in a nonmetallic base material or porosity in aluminum laser welds. Unfortunately, straightforward tools for an estimation of the defect response fields above the sample using pertinent detection concepts are still missing. In this study the Finite Element Method (FEM) was used for modeling spherically shaped defects and an analytical expression developed for the strength of the response field including the conductivity of the defect and matrix, the sensor to inclusion separation and the defect size. Finally, the results also can be useful for Eddy Current Testing problems, by taking the skin effect into consideration. Keywords. Electromagnetic Testing, Spherical Defects, Finite Element Method

Introduction When applying an electrical current flow within a given material using induction or injection techniques, variation of its spatial electrical conductivity distribution will impact the distribution of the electrical currents and their corresponding magnetic fields within and outside the tested sample, respectively. Significant conductivity changes can be observed in case of defect regions within the homogeneous material structure such as cracks, voids, shrink holes and inclusions. Among the common electromagnetic Nondestructive Testing methods Magnetic Particle Testing (MPT) has the lion’s share in routine testing applications. In comparison to Eddy Current Testing (ECT) MPT can be regarded as a pure surface inspection technique, whereas ECT provides a view at a significant depth of several mm below the sample’s surface, when using adapted testing equipment. The first use of MR sensors and other sensitive field sensors in NDT, like the SQUID [1-3], in the mid-90s opened the door for a new NDT research branch. An AMR sensor in ECT-probes was already investigated at the Federal Institute for Materials Research and Testing in 1995 [4]. It was the advent of a new magnetic micro systems generation after the discovery of the Giant Magneto Resistance effect (GMR) in 1988 that paved the way for new detection concepts in ECT as well as in flux leakage testing. This boom in GMR-research was also supported by the Nobel Prize in Physics in 2007 for the discovery of the GMR effect by Peter Grünberg and Albert Fert. Currently GMR sensors are being increasingly proposed to detect small defects

M. Kreutzbruck et al. / Magnetic Response Field of Spherical Defects

45

with a remarkable signal-to-noise ratio and high spatial resolution [5-8]. The results of this work meet this new research approach, in which the magnetic flux density B is detected directly by a field sensor instead of an induction coil which measures the corresponding field derivative with respect to time B/t. There exist a number of inclusion-related NDT problems such as tantalum inclusions hidden in niobium plates used for superconducting resonators or testing superconducting cables with their complex structure of micro filaments. The latter also involves the estimate of their size and position within the wire’s cross-section, which is vital for a reliable quality check. The problem posed by inclusions also needs to be addressed when testing aluminum laser welds involving spherical shaped and non-conducting pores representing a limiting case of the inclusion problem. A remarkable amount of theoretical work has been done in electromagnetic testing by the Eddy Current Testing community. Several approaches were devised by Bowler et al. to calculate cracks, voids and other inhomogeneities and their impact on a sensing coil [9]. However, these works are mainly concerned with zero conductivity defects and the changes in the detection coil’s impedance, and do not address the magnetic flux density.

1. Field calculations The most standard FEM codes for ECT problems use the so called [A, V-A]method, in which vector potential A and scalar potential V has to be found by solving the differential equation system [19, 20] for each node in the FEM mesh. From both of these quantities the electrical current density and the corresponding magnetic flux density can then be calculated. For the generation of a homogeneous current flow both an ultra-low frequency Eddy Current (EC) model and an injection model we used as well. The latter uses two potential boundary conditions at the left and the right edge of the sample applying a voltage and a corresponding homogeneous current flow. The EC method and the injection method yield the same results in most cases. It turned out that the numerical accuracy of the solver for alternating fields was somewhat higher than that of the dcsolver. For the calculation of the response field at great distances it was therefore preferred to calculate using ultra-low frequencies of MHz to simulate the dc-case.

Figure 1. left. The surface mesh of a metal plate showing the surface current density induced by a flat circular excitation coil. Right: Model of inclusions with different sizes (50 μm 800 μm in dia.), incorporated at the center of the niobium plate.

46

M. Kreutzbruck et al. / Magnetic Response Field of Spherical Defects

For the calculation we modeled a 4 mm-thick plate with a size of 50 mm  50 mm. Inclusions with a diameter ranging from 50 μm to 800 μm (see Fig. 1, right) were incorporated into the plate at depths between 1 mm and 3 mm. For the EC excitation we used either a circular coil (see Fig. 1, left) or a symmetric differential (not shown here) coil to achieve better homogeneity. The node density in the FEM mesh is distinctly enhanced at the spheres’ locations. This serves to adapt the distance between two nodes to the field gradients generated by the inclusions. The element size of a 50-μm-sized inclusion is in the order of 4 μm, whereas the edge elements of the metal plate yield dimensions of nearly 1 mm. For better visualization in Fig. 1, right, only the surface mesh of the tantalum spheres is represented, neglecting the spheres’ connection to the volume mesh of the matrix. The depth at which the inclusion is located can easily be shifted in the model. In the following we discuss the electrical and magnetic field variation generated by an inclusion with a conductivity i within a conductive host medium of conductivity M, carrying a uniform current density j0. For simplification we used the absolute value j  j  j ) for the current density, whereas we of all spatial current components ( j calculated only the vertical component of the magnetic flux density Bz, which usually is then detected by a field sensor. For inclusions showing a higher conductivity than that of the matrix, the currents will be focused into the inclusion, resulting in higher current densities at the front and back of the inclusion where the current flow direction is parallel to the normal vector of the inclusion surface. This is shown in Fig. 2, left or the case of a tantalum inclusion hidden in a niobium matrix. For low conductivity inclusions the situation is the opposite. Here the current is forced to flow around the inclusion and a minimum current density can be observed at the front and back (abutting face) with respect to the direction of the homogeneous current flow. The maximum of the distortion current strength occurs at the inclusionhost interface along the inclusion’s cross-section, which is aligned perpendicular to the current direction and runs through the center of the inclusion. If it is assumed that the currents run along the y-direction, this interface circle would pass through the following points in Fig. 2, left: (-0.4, 0, 0), (0, 0, 0.4), (-0.4, 0, 0), (0, 0, -0.4). In the 0

2 x

2 y

2 z

Figure 2. left: Eddy current distortion of a 2 mm deep circular tantalum inclusion (0.8 mm in dia.) located in a planar niobium sheet. Eddy current distortion in the x y plane. The current flows along the y axis. The conductivity of tantalum is somewhat higher than that of niobium, leading to increased distortion currents at the front side along the y axis at (0, 0.4, 0) and (0, 0.4, 0) and to reduced current densities at (0.4, 0, 0) and ( 0.4, 0, 0). Right: Current density j (jx²+jy²+jz²)0 5 in the vicinity of the inclusion at the x/y plane at z 0 (cut plane through the inclusion’s centre). Uniform current flow passes along x axis. Zero conductivity inclusion (200 μm in dia.) hosted in a Ti matrix ( 2.34 MS/m).

M. Kreutzbruck et al. / Magnetic Response Field of Spherical Defects

47

Figure 3. Current density j (jx²+jy²+jz²)0 5 in the vicinity of the inclusion (200 μm in dia.) along the x axis at z 0 (line through the inclusion’s centre). Uniform current flow passes along x axis. Left: upper curve (blue, dashed) represents Ti inclusion ( 2.34 MS/m) hosted in a Cu matrix ( 59.6 MS/m) and lower curve (red, solid) represents air inclusion hosted in an Al matrix ( 37.7 MS/m). Right: upper curve (red) represents Cu inclusion ( 59.6 MS/m) hosted in a Ti matrix ( 2.34 MS/m) and lower curve (blue) represents air inclusion hosted in a Ti matrix.

case of zero-conductivity inclusions, the enhancement of the current density is about 50% of the matrix current density, regardless of the inclusion’s size. Figures 2, right and Fig. 3 show that the presence of an inclusion affects the current distribution only in the close proximity of the inclusion. If the distance between the sensor and the inclusion’s surface is equal to the inclusion’s diameter (this is equal to three times the inclusion radius beginning from the inclusion center), the distortion currents are already attenuated to only 3 % of the maximum perturbation currents at the inclusion’s surface. Therefore the uniform current distribution only experiences a significant variation near the inclusion-host interface. For distances larger than the inclusion’s diameter, the deviations due to perturbation currents can be neglected. These results are in accordance with the work of G. Sepulveda et al. who also showed that the distortion of the uniform current distribution can be neglected for distances which are greater than three times the inclusion radius [21]. Figure 3 shows a line scan of the current distribution along the y-axis for diverse inclusion-matrix material combinations. Note that because of the shape of the inductor, the generated current flow was not exactly homogeneous, showing a slight linear rise along the path in Fig. 3, right. Because of the inclusion’s low conductivity, the current density outside the inclusion is higher than inside. In the case of a Ti inclusion hosted in a Cu matrix a small amount of current still flows through the titanium. On the other hand, if the inclusion conductivity is higher than that of the host, the currents will flow into the inclusion and Fig. 3, right indicates that this effect is somewhat higher. The Cu inclusion located within a Ti matrix shows significantly higher current densities compared to its air counterpart.

48

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2. Response for varied conductivity of inclusion and host We now take a look at the magnetic fields generated by the distortion currents and quantitatively determine how different inclusion conductivity and different host materials affect the current distribution and the corresponding magnetic field response. As materials for host and inclusion, Cu, Ti, Al and air with the following conductivity values have been used: titanium ( = 2,34 MS/m), niobium ( = 6,93 MS/m), and aluminum ( = 37,7 MS/m).

B z [μT]

5

I

2.5

<

I

> M

Ta

0 -2.5 -5 Nb-matrix, 6.93 MS/m

-7.5

Ti-matrix, 2.34 MS/m

10 10

3

10

4

10

5

10

6

10

7

10

8

10

9

conductivity inclusion [S/m]

Figure 4. left: Strength of the Magnetic field variation above the sample as a function of the inclusion’s conductivity. Two different host conductivities were used (black: Ti, 2.34 MS/m, grey: Nb, 6.93 MS/m). Inclusion diameter: 200μm, Sensor to inclusion separation: 5 mm. Each inclusion is located 2 mm below the surface. Solid lines represent the results of the fit function using Eq. 3. Right: Example of the field distribution for low and high conductivity inclusions.

In Figure 4 the maximum field magnitude (Bz, peak-to-peak amplitude) is shown for different compositions as a function of inclusion conductivity. In the case of inclusion conductivity smaller than that of the tested material, the induced currents which otherwise would pass undisturbed through the volume of the inclusion are perturbed and have to flow around the inclusion. The corresponding vertical component of the magnetic field is displayed in Fig. 4, top right (the effect of lowinclusion conductivity is shown to the left from the zero point). The situation is opposite when the inclusion conductivity is greater than that of the tested material. Then the currents flow from the host into the inclusion, leading to a change in the direction of circulation. The circular perturbation currents that once flowed clockwise now flow anti-clockwise (Fig. 4 right, on the right from the zero point and Fig. 4, right bottom). Consequently, the sign of the magnetic field is changed from positive field values to negative ones. When the conductivity of the inclusion and matrix are the same, this will obviously result in a vanishing response field and no perturbation currents will occur (zero point, Fig. 4, left). One can observe that for very low inclusion conductivity the defect response does not change significantly if the conductivity of the inclusion is further reduced. The same saturation effect occurs for very high inclusion conductivity. By comparing the field values for very low and very high defect conductivities one can observe an anomaly, already seen when dealing with the current distribution. In the limit of high

M. Kreutzbruck et al. / Magnetic Response Field of Spherical Defects

49

inclusion conductivity one finds a field response exactly twice as high as that of an inclusion with negligible conductivity. We define  as the ratio between the inclusion’s conductivity I and matrix conductivity M as follows:



I M

(1)

The numerical data for any M in the limit at infinity and zero conductivity show the following relation:

lim Bz 



lim Bz 

 2

(2)

0

The response field Bz of an inclusion with excellent electrical transport properties, say silver, in a low conductivity metal matrix will be higher than that of an air inclusion (pore) located in the same matrix carrying the same homogenous current density. The reason for these phenomena can be explained by the limited inclusion volume. The defect volume is limited with respect to the much larger volume of the host. Assuming that all currents are pushed out of the inclusion, it is not possible to increase the response field by lowering the inclusion conductivity. It is therefore reasonable to assume that for the virtually infinite volume of the matrix significantly more current can be passed through the inclusion if its conductivity is high enough. Of course, there also exists an optimum path for the currents flowing from the host into the inclusion and back again. The simulation reveals that this geometrical condition causes a response field which is a factor of 2 larger than that of the zero conductivity case. A fit of the numerical data shows that   M  1  (3)  Bz ~ I   I  2 M   2  When using the FEM results (dots in Fig. 4, left) we found the error of this analytical expression (solid line in Fig. 4, left) to be below 2%. Note that these results are independent of the inclusion’s size or the distance of the sensor above the sample’s surface.

3. Sensor-to-Inclusion Separation and Inclusion Size In Figure 5, left, the magnetic field is shown as a function of the sensor-to-inclusion separation z, in which z describes the distance between the centre of the inclusion and the field detecting area of the sensor. In addition, for better visualization of the fall-off behavior, Fig. 5, right shows the ratio of B(z/2)/B(z), which is denoted by  in the following sections. The simulation was carried out for inclusions with sizes ranging between r = 100 μm and r = 800 μm. The sensor-to-inclusion separation is divided into two regimes both of which show a different fall-off characteristic of 1/z. Starting in the very near field regime at the inclusion’s centre we see that  is distinctly below 2. By approaching the inclusion’s surface  converges to 2. By exceeding the interface of the inclusion and the matrix, the fall-off characteristic shows the quadratic behavior in which  = 2 because of the quantity B(z/2),  = 4  = 2) that is not achieved at the surface at once. It is only obtained when

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M. Kreutzbruck et al. / Magnetic Response Field of Spherical Defects

distances are at least twice the inclusion’s radius. Closer examination of the data shows that the interface of the two regimes  < 2 and  = 2 is located exactly at the inclusionhost interface. The simulations also confirm that Bz as function of the inclusion radius r scales exactly with a r³ law. This also can be seen in Fig. 5, left, where the magnetic field response is distinctly increased in the presence of larger inclusions. Furthermore, the graph shows that a larger inclusion diameter will shift the regime of  < 2 towards higher values. Independent of the inclusion size, the  = 2 regime invariably is entered at the interface of inclusion and host.

Figure 5. Fall off characteristics calculated for different inclusion diameters. Magnetic field variation as a function of the sensor to inclusion separation (left) and ratio of Bz(z/2)/ Bz(z) as function of the dipole to sensor separation (right). Inclusion with zero conductivity (air) located in a titanium matrix ( 2.34 MS/m).

4. Analytical Expression for the Response Field Bz Size dependence and spacing between sensor and inclusion are in good accordance with the results of G. Sepulveda et al. [21]. They used spheroidal shaped cracks with variable conductivity to analytically calculate the magnetic field that would be measured by a magneto sensor. Due to the complexity of the problem, the solution is given only for the dc-problem and is a first-order approximation. The general solution is proportional to the Legendre functions of the first kind and consists of odd Legendre polynomials. One can use several boundary conditions to determine the coefficients, but due to the limited number of boundary conditions, only first terms of the polynomial expansion can be used. The spheroidal approach is hereby a kind of approximation, which makes an analytical calculation of the current distribution possible. However, when turning to the magnetic field, unfortunately no unique mathematical expression can be derived, leading also to finite element approaches. Thus no expression of the field strength for different inclusion conductivity was presented. Our FEM results are in good agreement with the current and field distribution of G. Sepulveda, who also found that the magnitude of the far field – distances much further than the prolate spheroid’s diameter – falls off as 1/R2 at any given direction. Implementing the findings of sections 3 and 4 we now present a simple analytical expression for varying conductivity in the inclusion and the matrix, which fits the numerical data extremely well for all types of isotropic materials:

M. Kreutzbruck et al. / Magnetic Response Field of Spherical Defects

Bz pp  

0 1.354

 j0 

r3  1    z2   2 

51

(4)

To provide a broad data set, we calculated the peak-to-peak magnetic flux density Bz pp for a number of different inclusions. The sensor-to-inclusion separation was varied in the regime ranging from z = 2 mm to z = 6 mm. The radius of the inclusions was varied between 50 μm and 400 μm. Finally for the inclusion conductivity we used values between 0 MS/m and 59.9 MS/m (Cu) and for the conducting host we used values ranging from the conductivity of Ti to that of Cu. As a result, Bz pp varies between 30 pT and 7 μT, covering almost 6 orders of magnitude. Despite this high dynamic field range, the constant k = μ0/1.354  9.28 10-7 Tm/A only varies in a range of a few percent (see Fig. 6).

FIGURE 6. Variation of k for different inclusion types. Left axis: absolute value of k. Right axis: Relative error assuming k to be 9.28 10 7. Ti:  2.34 MS/m, Al:  37.7 MS/m, Cu:  59.9 MS/m. Sample 1 4 : i 0 , M Ti , zi 3,5,4,5 mm, r in μm; sample 6 9: i 0, M Al , zi 3,4,3,5 mm, r in μm; sample 11 14: i 0, M Ti , zi 2,3,4,5 mm, r 50 μm; sample 16 18: i 0, M Ti , zi 2,3,4 mm, r 100 μm; sample 20 22: i 0, M Ti , zi 3,4,6 mm, r 200 μm; sample 24 26: i 0, M Ti , zi 2,4,5 mm, r 400 μm; sample 28 32: i in MS/m, M Ti , zi 5 [mm], r 100 μm; sample 33 36: i, M , zi 4,5,4,5 mm, r 100 μm.

5. Conclusion In routine non-destructive testing applications the estimation of the detectability of different material defects is a common task in choosing the proper testing method. The signal strength generated by inhomogeneities within the material being tested should be beyond the noise level either caused by the electronic noise of the testing device or the intrinsic noise sources of the sample itself, such as local variation of the conductivity or permeability due to the material’s microstructure. The analytical expression derived from the FEM-results will facilitate the estimation of the signal strength caused by spherical inclusions and requires the current density, sensor-to-inclusion separation, inclusion size the conductivity of matrix and inclusion. Finally, the question should be

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addressed as to how these results can be transferred to alternative defect types like porosities and cracks. We found in further investigations that the qualitative behaviour of the magnetic field does not change significantly for more elongated flaws. Even for pure rectangular cracks with high aspect ratio the magnetic field above the sample’s surface can be interpreted as being generated by a dipole-like source with its 1/z² characteristics - a result also found by Sepulveda. However, for the absolute signal strength we found a stronger influence of the cross-section and the current direction compared to the influence of the crack width. This relation still has to be further investigated. Meanwhile there exist a series of NDT activities, with which the proposed analytical expression can be confirmed by experimental data [2,8]. A systematic validation of these theoretical results will be a future task.

References [1] M. v. Kreutzbruck, J. Tröll, M. Mück, C. Heiden and Y. Zhang Trans. Appl. Supercond.7, 3279, IEEE, 1997. [2] M. Mueck, C. Welzel, F. Gruhl, M. v Kreutzbruck, A. Farr, F. Schoelz, Physica, C 368 96 99 (2002). [3] H. J. Krause and M. v. Kreutzbruck, Physica C 368 70 79 (2002). [4] M. Stoppel, D. Filbert, H. M. Thomas, Research report at Technical University Berlin and Federal Institute of Materials Research and Testing, May 1995. [5] C. H. Smith, R. W. Schneider, T. Dogaru, S. T. Smith, Rev. Prog. in QNDE, 22, 419 426, (2003). [6] B. Wincheski, M. Namkung, Rev. Prog. Quant. Nondestr. Eval. 509, 465 (2000). [7] K. Allweins, M. v. Kreutzbruck, G. Lembke, J. Appl. Phys. 97, 10Q102 (2005). [8] M. Kreutzbruck, H. Bernau, K. Allweins, TM-TECHNISCHES MESSEN , 75 (9) p. 477 484 (2008). [9] J. R. Bowler, J. Appl. Phys. 75 (12) 8128 (1994). [10] J. R. Bowler, S.A. Jenkins, L.D.Sabbagh, and H.A. Sabbath, J. Appl. Phys. 70 (3) 1107 (1991). [11] N. Harfield, Y.Yoshida and J. R. Bowler, J. Appl. Phys. 80 (7) 4090 (1996). [12] A.P.Raiche , J.H. Coggon, Geophys J. R. Astron. Soc. 42, 1035 (1975). [13] J. R. Bowler, J. Appl. Phys. 86 (11) 6494 (1999). [14] S. M. Nair and J.H. Rose, J. Appl. Phys. 70 (4) 1924 (1991). [15] C.T. Tai, Dyadic Geens’s Functions in Electromagnetic Theory (Intex, Scranton, 1971). [16] P.E. Wannamaker, G.W. Hohmann, and W.A. SanFilipo, Geophysics 49, 60 (1984). [17] B. J. Roth, N. G. Sepulveda, and J.P Wikswo, Jr., J. Appl. Phys. 65 (1) 361 (1989). [18] R.E. Beissner, J. Appl. Phys. 60 (1) 352 (1986). [19] A. Kost, Numerische Methoden in der Berechnung elektromag. Felder, Springer Verlag (Berlin) (1994). [20] S.C. Brenner, L.R. Scott, The Mathematical Theory of Finite Element Methods, Springer Verlag, 2002. [21] N. G. Sepulveda, J. P. Wikswo, Jr., J. Appl. Phys. 79 (4) 2122 (1996).

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-53

53

Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking from EddyCurrent Signals Ladislav JANOUSEK 1, Milan SMETANA, Marcel ALMAN Department of Electromagnetic and Biomedical Engineering, Faculty of Electrical Engineering, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovak Republic

Abstract. The paper deals with uncertainty in depth estimation of partially conductive cracks from eddy current testing signals. Numerical simulations are carried out to investigate influences of crack parameters on the response signals. Three parameters of the crack, i.e. its depth, width and conductivity are changed to simulate variety of possible scenarios. Standard pancake probe is used for the inspection at first. The presented numerical results confirm that the inverse problem is highly ill posed when partially conductive cracks, as stress corrosion cracking, are concerned. Accordingly, a new approach in the response signal sensing is proposed. The idea is to pick up more information provided by the eddy currents. Thus, three coils positioned perpendicularly to each other are employed to sense all the three spatial components of the perturbation electromagnetic field. The gained results reveal that it is possible to considerably decrease the uncertainty in depth estimation of partially conductive cracks by employing the proposed idea. Keywords. non destructive evaluation, eddy currents, partially conductive cracks, depth estimation, uncertainty

Introduction System health monitoring (SHM) and condition based maintenance (CBM) are of high interest nowadays in order to sustain safety, reliability and quality of various processes. Non-destructive evaluation plays accordingly the key role in SHM and CBM where not only reliable detection but also precise estimation of dimensions of a detected anomaly is required. Enhancing non-destructive evaluation methods is therefore very important for accomplishing their challenging missions. Different physical principles are utilised for the non-destructive inspection and evaluation of materials. Eddy current testing (ECT) is one of the widely utilized electromagnetic methods. It originates from the electromagnetic induction phenomena and its principle underlies in the interaction of induced eddy currents with structure of an examined body. Perturbations in eddy currents distribution due to a presence of an anomaly are detected. Indisputable advantages of the method such as high inspection speed, high sensitivity for surface breaking cracks, versatility account for gradually 1

Corresponding Author: Ladislav Janousek, Department of Electromagnetic and Biomedical Engineering, Faculty of Electrical Engineering, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovak Republic; E mail: [email protected]

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L. Janousek et al. / Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking

increasing employment of the method in practical applications, especially in nuclear, petrochemical and aviation industries. However, interpretation of the ECT signals is rather difficult as the inverse problem is ill-posed [1]. The progress in powerful computers has allowed development of automated procedures to evaluate dimensions of a detected anomaly in ECT. In general, two approaches are utilized for the purpose, deterministic and stochastic ones [2-6]. Usually, one dimensional signal gained by scanning just above a crack along its length is taken as an input to the evaluation procedure. Mostly, three variables of the crack are estimated, its depth, length and a position of its centre, while a profile, a width and the electromagnetic properties of the defect have to be adjusted in advance. Satisfactory results are reported by several groups for evaluation of artificial slits [3], even of several close parallel notches [6]. However, evaluation of real cracks, especially stress corrosion cracking (SCC) from ECT response signals remains still a challenge [3], [7]. SCCs are quite different comparing to artificial slits or even to other types of real defects. Cross sections of SCC frequently show branched structure and group of cracks usually occur in what is known as a colony. The local opening of SCC is usually very small, e.g. tens of micrometers; however a damaged region itself is much broader. SCC contains many unbroken ligaments both in depth and opening directions what makes SCC partially conductive and in this case its width has to be also considered [8]. It means that additional variables should be taken into account for evaluation of a detected SCC what considerably increases ill-posedness of the inverse problem [1]. Thus, many unsatisfactory results are reported when the automated procedures originally developed for non-conductive cracks are employed in the evaluation of SCC [3], [7]. It is stated that one of the possible reasons is lack of sufficient information [3]. The authors propose a new idea in sensing eddy currents response signals in order to decrease uncertainty in SCC evaluation. The vector lines of the eddy-current density are closed themselves, because the divergence of the eddy-current density vector equals to zero in an inspected material. Thus, any electromagnetic anomaly at present influences the path of eddy-currents in quite complicated manner and creates perturbations in the resulting electromagnetic field. Even, many ECT probes have been developed over past decades reflecting special demands of particular applications, they are usually designed in such a way that only one component of the perturbation field is sensed. However, curved paths of eddy-currents provide more information. The authors’ proposal is to sense all the three spatial components of the perturbation field to gain three separate signals of a same crack. Two-dimensional scan over a cracked region is required in this case. Numerical investigations are carried out to prove effectiveness of the proposal. Varieties of non-conductive as well as partially conductive cracks are modelled to study their influence on the perturbation field. The paper presents the gained results and their evaluation.

1. Numerical Model A plate specimen having the electromagnetic parameters of a stainless steel SUS316L is inspected in this study. The specimen has a thickness of t = 10 mm, a conductivity of σ = 1.4 MS/m and a relative permeability of μr = 1. A surface breaking crack appears in the middle of the plate. It is modelled as the cuboid having different electromagnetic properties from the base material. Configuration of the plate with the crack is shown in Figure 1.

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L. Janousek et al. / Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking

z SUS316L

y

wc

x lc dc

σc

10

σ = 1.4 MS/m μr= 1

Figure 1. Configuration of plate specimen with crack

The numerical calculations are performed using the edge-element code. Three parameters of the crack are varied in other to simulate various structures of real cracks. The crack depth dc is changed from 1 mm up to 10 mm with a step of 1 mm, its width wc is adjusted to five values ranging from 0.2 mm until 1.0 mm with a step of 0.2 mm and the conductivity of cracked region σc is set to 0, 1, 2, 5, 10% of the base material conductivity. Length of the crack is kept at a constant value of lc = 10 mm for all the cases. Frequency of the harmonic driving signal is adjusted to f = 10 kHz. An ECT probe scans 1 mm above the plate surface. Influences of the crack parameters on the ECT response signals are studied. The results are presented and discussed in the following sections.

2. Standard Approach The standard self-inductance absolute pancake probe is employed for the inspection of the specimen with crack at first. The circular coil is positioned normally regarding the surface of plate. Its axis is parallel to the z-axis of the coordinate system shown in Figure 1. Inner diameter of the coil is 4 mm, the outer one has a value of 8 mm and a height of the winding is 2 mm. 05

04

1 mm 3 mm 5 mm

1 mm 3 mm 5 mm

03

04

imaginary [mV]

absolute value [mV]

02

03

02

01 0 01 02

01 03 04

0 20

15

10

5

0

5

10

15

probe position [mm]

a) absolute value vs. probe position

20

04

03

02

01

0

01

02

real [mV]

b) signal in complex plane

Figure 2. Crack response signal influence of crack depth

03

04

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L. Janousek et al. / Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking

The inspection is realised in a standard way; one dimensional scanning with the probe over the crack centre along its length is performed. The response signal is calculated for the various parameters of the crack. Figure 2 shows the response signal for the non-conductive crack with depths of dc = 1, 3, 5 mm and a width of wc = 0.2 mm. Similar results are displayed in Figure 3. The crack has a depth of dc = 3 mm, a width of wc = 0.2 mm and conductivities of σc = 0, 5 and 10% of the base material conductivity. Influence of the crack width on the response signal for partially conductive crack with a conductivity of σc = 5% of the base material conductivity and a depth of dc = 3 mm is shown in Figure 4. These results are gained for the crack widths of wc = 0.2, 0.6, 1.0 mm. 04

04

0% 5% 10%

02

imaginary [mV]

03 absolute value [mV]

0% 5% 10%

03

02

01 0 01 02

01

03 04

0 20

15

10

5 0 5 probe position [mm]

10

15

04

20

03

02

01

0

01

02

03

04

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04

real [mV]

b) signal in complex plane

a) absolute value vs. probe position

Figure 3. Crack response signal influence of crack conductivity 04

04

0 2 mm 0 6 mm 1 0 mm

02

imaginary [mV]

03 absolute value [mV]

0 2 mm 0 6 mm 1 0 mm

03

02

01 0 01 02

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03 04

0 20

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probe position [mm]

a) absolute value vs. probe position

15

20

04

03

02

01

0

01

02

real [mV]

b) signal in complex plane

Figure 4. Crack response signal influence of crack width

It can be seen that the response signal is the complex variable of all the considered crack parameters. Figure 5 demonstrates quite high uncertainty in depth evaluation of partially conductive cracks. In this case only the maximum points of the response signals are plotted for the crack with three depths of dc = 1, 3, 5 mm and all the considered widths and conductivities. As it can be observed the crack signals of the crack with the three different depths are highly overlapped and thus under- or overestimation of the crack depth can occur with high probability. Especially, the underestimation can bring serious consequences in many applications.

L. Janousek et al. / Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking

0

57

1 mm 3 mm 5 mm

imaginary [mV]

01

02

03

04

05 0

01

02

03

04

05

real [mV]

Figure 5. Overlap of response signals due to partial conductivity of cracked region

The reason of the high uncertainty in depth estimation of partially conductive cracks using standard ECT probes and procedures is lack of sufficient information. The next section introduces a new idea for the response signal sensing to increase information content of the signal.

3. Proposal of New Approach The vector lines of the eddy-current density must be closed themselves in an inspected material. Thus, any electromagnetic anomaly at present influences the path of eddycurrents in quite complicated manner and creates perturbations in the resulting electromagnetic field. The previous section clearly showed that the degree of uncertainty in depth evaluation of a partially conductive crack is quite high when only one component of the perturbation field is sensed; however, the eddy currents provide more information. The authors propose sensing all the three spatial components of the perturbation electromagnetic field to increase the information rate of ECT response signals. Numerical results are provided to support the proposal. The same coil as in the previous section drives the eddy currents in the specimen. Three circular coils of same dimensions, i.e. the outer diameter equals to 4 mm, the inner one is set to 2 mm and the height of winding is 0.5 mm, sense the response signals independently. The coils are positioned perpendicularly to each other to sense all the three spatial components of the perturbation field. All the coils are centred at one point. The numerical simulations are performed under similar conditions as described in the previous section; however two dimensional scanning over the cracked region is realized. The response signal gained with the detecting coil oriented along the x-axis according to the coordinate system shown in Figure 1 is denoted as the x- component. Accordingly, the response signals sensed with the detection coils oriented along the y-axis and z-axis are labelled as the y- component and the z- component, respectively. Figure 6 displays the response signals for the non-conductive crack with a width of wc = 0.2 mm and a depth of dc = 3 mm. As it can be seen, each component provides some information about the inspected defect; however, x- and y- components have lower level than the z- component.

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L. Janousek et al. / Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking

absolute value [mV]

absolute value [mV] 0.05 0.04 0.03 0.02 0.01 0

0.03 0.02 0.01 0

20 15 10 5 0 x [mm]

15 5 10 15 20 20

10

5

0

5

10

15

20 20 15 10 5 0 x [mm]

y [mm]

a) x- component

15 5 10 15 20 20

10

5

0

5

10

15

20

y [mm]

b) y- component

absolute value [mV]

0.3 0.2 0.1 0

20 15 10

5 0 x [mm]

5

15 10 15 20 20

10

5

0

5

10

15

20

y [mm]

c) z- component Figure 6. Crack response signal gained using proposed detector

Particular numerical results are presented in Figure 7. Only maximum points of the sensed signals are shown in the plots. Signals of the x- and the y- components are magnified by factor 5 to be able to display them in a same plot together with the zcomponent because of the reason mentioned above. Figure 7a) presents influence of the crack depth on the response signals amplitudes. Only signals amplitudes of the nonconductive crack with a width of wc = 0.2 mm and depths dc ranging from 0 to 9 mm with a step of 1 mm are depicted. Figure 7b) displays the results for various values of the crack conductivities; σc = 0, 1, 2, 5, 10% of the base material conductivity. The other parameters of the crack are adjusted to the following values wc = 0.2 mm, dc = 3 mm in this case. The influence of the crack opening on the crack signals amplitudes is shown in Figure 7c). The partially conductive crack with a relative conductivity of σc = 5% and a depth of dc = 3 mm is considered here. Its width wc is varied from 0.2 mm up to 1.0 mm with a step of 0.2 mm. It can be observed from the results shown in Figure 7 that each component behaves in slightly different manner when changing parameters of the crack, i.e. its depth, width and conductivity. It seems from Figure 7a) that the x- component is more sensitive to the crack depth comparing to the other two components. It even does not saturate so quickly with increasing depth of the near-side surface crack. The reason can be explained from the nature of eddy current lines’ changes due to a presence of crack. The x- component is especially formed by the perturbation field arising from eddy currents flowing around tips of the crack that is higher than in the other two axes. On the other side, Figures 7b) and 7c) show that the conductivity and the width of crack influences more the y- component than the two other components as a sensitivity

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L. Janousek et al. / Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking

of the y- axis coil to the perturbation field arising from eddy currents flowing through a partially conductive crack is highest comparing to the sensitivity of the pick-up coils in the other two axes. It can be concluded that sensing all of the three spatial components of the perturbation field can increase information rate of the ECT response signals. This is especially advantageous when partially conductive cracks, like SCCs, can appear in an inspected structure and dimensions of the cracked region need to be evaluated. Degree of uncertainty in depth estimation of such cracks can be reduced by employing the proposed approach. 0

x component y component z component

0.4

01 imaginary [mV]

0.2

imaginary [mV]

x component y component z component

0 05

dc 0

σc

0 15 02 0 25

0.2 03 0 35

0.4

04

0.4

0.2

0

0.2

0

0.4

0 05

01

real [mV]

0 15

02 0 25 real [mV]

03

0 35

04

b) influence of crack conductivity

a) influence of crack depth 0 0.05 0.1 imaginary [mV]

wc 0.15 0.2 0.25 0.3 x component y component z component

0.35 0.4 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

real [mV]

c) influence of crack width Figure 7. Amplitude of crack response signal gained using proposed detector

Conclusion The paper focused on degree of uncertainty in depth evaluation of a detected crack from eddy current testing signals. The investigations were done from numerically calculated signals. Non-conductive as well as partially conductive cracks were concerned here. Three parameters of a crack were varied, i.e. its depth, conductivity and width. Standard pancake probe was employed for the inspection at first. The presented results demonstrated that the inverse problem is highly ill-posed when only one component of the perturbation field is picked-up for a single scanning line just

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L. Janousek et al. / Decreasing Uncertainty in Size Estimation of Stress Corrosion Cracking

above a crack along its length. Consequently a new inspection approach was proposed in the paper. It comes from the fact that more information about a detected crack can be gained by sensing all of the three spatial components of the perturbation electromagnetic field. Two dimensional scanning is required in this case. It was shown that the response signals sensed with three coils that are oriented perpendicularly to each other behave in slightly different way when changing the parameters of crack. This is advantageous as degree of uncertainty in depth evaluation especially of partially conductive cracks, as stress corrosion cracking, can be reduced in this way. Further work is going to be concentrated on experimental verification.

Acknowledgements This work was supported by the Slovak Research and Development Agency under the contract No. APVV-0194-07. This work was also supported by a grant of the Slovak Grant Agency VEGA, project No. 1/0308/08.

References [1] N. Yusa, H. Huang, K. Miya, Numerical evaluation of the ill posedness of eddy current problems to size real cracks, NDT&E International 40 (2007), 185 191. [2] G. Rubinacci, A. Tamburino, S. Ventre, Fast numerical techniques for electromagnetic nondestructive evaluation, Nondestructive Testing and Evaluation 24 (2009), 165 194. [3] N. Yusa, Development of computational inversion techniques to size cracks from eddy current signals, Nondestructive testing and evaluation 24 (2009), 39 52. [4] Z. Chen, N. Yusa, K. Miya, Some advances in numerical analysis techniques for quantitative electromagnetic nondestructive evaluation, Nondestructive testing and evaluation 24 (2009), 69 102. [5] B.P.C. Rao, An artificial neural network for eddy current testing of austenitic stainless steel welds, NDT&E International 35 (2002), 393 398. [6] M. Rebican, Z. Chen, N. Yusa, L. Janousek, K. Miya, Shape reconstruction of multiple cracks from ECT signals by means of a stochastic method, IEEE Transactions on Magnetics 42 (2006), 1079 1082. [7] N. Yusa, L. Janousek, M. Rebican, Z. Chen, K. Miya, N. Dohi, N. Chigusa, Y. Matsumoto, Caution when applying eddy current inversion to stress corrosion cracking, Nuclear Engineering and Design 236 (2006), 211 221. [8] N. Yusa, K. Miya, Discussion on the equivalent conductivity and resistance of stress corrosion cracks in eddy current simulations, NDT&E International 42 (2009), 9 15.

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-61

61

Semi-Discrete Time-Domain Sensitivity Analysis For Cracks Recognition

Konstanty M. GAWRYLCZYK West Pomeranian University of Technology in Szczecin, Poland Department of Electrotechnology and Diagnostics Abstract. Semi discrete method is known since 80’s of XXth century. The method provides analytical solution in time, so the time stepping may be omitted. Comparing to usual finite elements method in time, this method seems not to be numerically effective, because produced matrices are dense. Because of this reason, it was rather rarely used. However to carry out sensitivity analysis with adjoint models [1] solutions in forward and backward time have to be obtained. Both time points should coincide. For space discretization finite elements are used, as usual. The semi discrete method allows to determine analytically the continuous solution for any given time of analysis. In this paper evaluation of this method for different kinds of excitation shapes is presented. The sensitivity analysis is applied for inverse task of recognition of conductivity distribution in non destructive testing of materials using eddy currents. Keywords. Time domain field analysis, sensitivity analysis, cracks recognition.

Introduction The proposed semi-discrete method allows obtaining time-domain solution without time-stepping. For space discretization triangular finite elements of first order are used. The proposed method is used for algorithms of non-destructive testing (NDT) using eddy-currents. The excitation currents used by NDT in time domain have usually the shape of rectangular impulse or single sinusoidal impulse. The numerical solutions for both current shapes are listed below. For identification of crack shape the iterative algorithm is given, based on measurement of coil voltage moving over the crack and sensitivity analysis. To calculate sensitivity the Tellegen’s method is applied. The derivation of sensitivity equations in time domain one can find in autor’s earlier works, e.g. [1], while the sensitivity equations for frequency domain in [4]. The semi-discrete method delivers analytical and continuous solution for any given time of analysis, which has a form of exponential functions. In order to obtain an analytical formula, the integration of the sensitivity equation is necessary. The paper finds possible solutions of this problem, either the application of Zassenhaus formula or improvement of commutational properties of two matrices. The resultant gradient information may be used for solving inverse problems, such as identification of material conductivity distributions.

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K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition

1. FE-TS analysis Electromagnetic field diffusion into conducting region for two-dimensional models may be described by vector magnetic potential A:

‹2 A μγ

sA  0 ¸i t  f t . st

(1)

Approximating (1) with finite elements and applying time-dependent elements the solution with well known Finite Element – Time Stepping method is obtained, leading to the following system of linear equations:

 ¬ žžΘ¸ K M ­­¸ A ti 1  žŸ Δt®­ M ¬  Θ¸ f ti 1 1Θ ¸ f ti žž  1Θ ¸ K ­­­¸ A ti , žŸ Δt ®

(2)

with: K – stiffness matrix, M – mass matrix, t – time step, i - time index and 0,5    1 defines the differential scheme of the time stepping method. The effective solution of (2) is as long possible, as the time step t remains constant. In other case, matrix decomposition should be renewed. If there is the need to calculate the sensitivities of measured voltage versus material parameters, adjoint models are used [1], which appear in Tellegen’ theorem. The quantities relating to adjoint models are denoted by the index (+). Time moments from the analysis of adjoint model should coincide with that of original model. Because the adjoint model is analyzed applying reverse time, fulfillment of this condition may lead to excessive time steps and very long computational time. This is the reason, why the semi-discrete method has been elaborated. It allows to calculate the solution for any desired time moments, not only equidistantly placed.

2. Semi-discrete finite element analysis The inhomogeneous diffusion equation to be solved has the form of

[ K ]{A(t)} + [ M ]

∂A(t) = { f (t)}. ∂t

(3)

The solution is calculated as superposition of transient (t) component and steadystate solution (s) of A = As + At . Steady-state solution depends on the shape of excitation f(t). Transient component results from homogeneous equation:

sAt (t) 0 , st

\At (t)^ <M > which solution is

(4)

K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition

\At (t)^ \C^¸exp t¸< M > , with: \C^constant of integration. 1

63

(5)

The constant C depends on initial value A(0), which is zero in our case, and also on the excitation shape. The solutions for different excitations f are shown below.

3. Unit-step excitation However the current exciting a coil can not take a form of unit-step 1(t), it is handy approximation of the real shape of current. The steady-state response of the magnetic vector potential As in this case has the form: 1

1

\As (t)^< K > \ f (t)^ ¸1 t .

(6)

The constant of integration C can be evaluated from the initial condition

\As (0)^ \At (0)^\A(0)^0

(7)

and the semi-discrete solution for vector magnetic potential takes the form:

{ A (t )} = ([1] − exp ( −t [ M ] [ K ]) ) ⋅ [ K ] {1(t)} . −1

−1

(8)

Because of mass matrix inversion, (8) cannot be applied for the whole region. Outside the conducting region the mass matrix contains zeroes on main diagonal and for this reason becomes singular. The region has to be divided our into a conductive part “1” and a non-conductive part “2”:

 K ¡ 11 ¡K 21 ¢

£¦ s ²¦ K12 ¯¦£¦ A1 t ¦²¦  M11 0¯¦ A1 t ¦¦ ¦¦£ 0 ¦¦² ¦ °¤ ¡ ° » ¤st » ¤ ». ¦ ¦ f2 ¦ K 22 ±°¦¥¦A2 t ¦¼¦ ¢¡ 0 0±° ¦¦ ¦¥ 0 ¦¦¼ ¥¦ ¼¦

(9)

It is assumed that excitation currents are located only in a non-conducting part of the region. Then the following matrix equation for the conductive region is obtained:


11

> \A1 (t)^ <M11>\sA1 (t)/st^ 1

1

 \ f2 (t)^, or: \A1 (t)^ <M11>\sA1 (t)/st^\ fc (t)^.

(10)

The similarity of (10) to (3) allows for exploitation of solution (8). The correctness of described method was proved using very simple 2D-model (Fig. 1). The model consists of conducting region, air and linear excitation current. The material parameters are given on the picture.

64

K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition

Figure 1. 2D model for proof of semi discrete method

Figure 2. Comparison of A in node “1” for ti

Comparison of magnetic vector potential Ai (i - means the index of time moment) calculated using traditional FE-TS method and semi-discrete method is shown in Fig. 2. The comparison done for other nodes seems similarly.

4. Harmonic excitation For harmonic excitation there is the following inhomogeneous differential equation:

sA(t) \I m sin(ωt)^ . st

\A(t)^ <M >

(11)

The steady-state response As may be evaluated in frequency-domain using standard FEM:

K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition

65

1

\As^ jω¸<M > \ǿ^,



(12)



1

\As (t)^imag jω¸<M > ¸\ǿ^¸exp(jωt) .

The constant of integration C for transient component At (Eqn. 5) will be similarly evaluated, as described by Eqn.7 and assuming zero initial condition:



1



\C^imag jω¸<M > ¸\ǿ^ imag As .

(13)

Therefore, the semi-discrete solution for transient magnetic vector potential in presence of harmonic excitation equals:

\A(t)^imag As ¸exp(jωt) imag As ¸exp t¸<M > . 1

(14)

Obtained formula was tested using the same model as this shown in Fig.1. In Fig.3 there are solutions obtained with FE-TS, with proposed semi-discrete method and the steady-state shape of potential for node number 1. “i” means the time-moment index.

Figure 3. Comparison of magnetic vector potential in node “1” for harmonic excitation

5. Excitation with the rectangular impulse The solution for rectangular impulse was achieved as superposition of solutions for two unit-step impulses:

£¦(<1>et<M11>1 )¸ K 1 1(t) if t b T , < > \ ^ ¦ \A t ^¦¤¦  t-T <M11>1 t<Mc 11>1 1 ¦¦¥(e )¸ \1(t)^ otherwise. e

(15)

66

K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition

6. Single sinusoidal pulse The solution for single, sinusoidal current pulse was derived in the same manner, using superposition of two solutions given by Eqn.(14):





1 £¦ t¸<M > if tbT , ¦¦imag As ¸e jωt  As ¸e \A(t)^¦¤ 1 1 ¦¦  tT <¸ M > t¸ M K  As ¸e < > < > otherwise. ¦¦imag As ¸e ¥

(16)



The comparison done for test models reveals good conformity of solutions obtained using semi-discrete method versus this from classical FE-time-stepping.

7. Semi-discrete sensitivity analysis To perform inverse task basing on sensitivity analysis there has to be calculated sensitivity of voltage induced in the coil versus conductivity in finite elements Ȗ, it means the left’ hand side of equation (17). The term on the right-hand side of sensitivity equation (17) denotes the sensitivity components coming from finite elements. This sensitivity equation for time domain was derived in [1]. (+) denotes value related to adjoint model. T

T

0V

0V

+ + ³ ³ ( J 0 (τ ) E ( t ) ) dV dt = ³ ³ E ( t ) γ E (τ ) dV dt.

(17)

Integration of the product of electric intensity vectors over the finite elements of first order requires the Gaussian quadrature of the second order. Because Gaussian points are located on the element borders in this case, the products containing combinations of nodal values should be calculated. To obtain all necessary products, the following matrix R is defined: T

T

( ) ⋅{i }⋅ exp ( −IJ [ K ][ M ] ) ⋅ {i })

R = Δ ³ E + (τ ) ⋅ E (t ) dt = ³ [ M11 ] exp −t [ K c ][ M11 ] T

0

−1

0

(

⋅ [ M11 ]

−1

−1

c

−1

c

11

+ c

T

(18)

dt

where Δ  is the size of finite element. The matrix R can be rewritten as follows: T

( ) ⋅{i }⋅{i } ⋅ exp ( −IJ [ K ][ M ] ) dt,

R = Δ ⋅ ³ [ M11 ] exp −t [ K c ][ M11 ] −1

0

⋅ [ M11 ]

−1

−1

c

−1

c

11

+ T c

(19)

67

K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition −1

(

−1

because the term [ M11 ] exp −IJ [ Kc ][ M11 ]

) is symmetric. A drawback of the { }

established definition is that R is singular (it contains a singular term [ I c ] = {ic } ⋅ ic+

T

).

For better numerical efficiency, analytical integration would be essential. Since simple disentangling of exponential functions in (19) is impossible, two following methods for this purpose are proposed.

8. The Zassenhaus formula The Zassenhaus formula [3] is a version of the Baker-Campbell-Hausdorff formula. It can be written involving commutator nestings:

exp( X ) ⋅ Y ⋅ exp( − X ) = Y + [ X ,Y ] + where: [ X ,Y ] = X ⋅Y − Y ⋅ X .

1 [ X , [ X ,Y ]] + 1 ¬ª X , [ X , [ X ,Y ]]¼º + ... , (20) 2! 3!

In our case:

X = −t [ K c ][ M11 ]

−1

and Y = {ic } ⋅ {ic+ } ⋅ [ M11 ] = [ I c ] ⋅ [ M11 ] . −1

T

−1

(21)

If 1/M is the norm of matrices X and Y, an error of the Zassenhaus approximation is of the order O(1/M 2). It means that sensitivity calculations based on the Zassenhaus formula converge only for short times t, dependent on the norm of matrix [Kc][M11]-1. In practical calculations the convergence is obtained at the beginning of the transient process only.

9. Improvement of matrix commutations By applying the Zassenhaus formula for two good commuting matrices, the result is

exp( X ) ⋅Y ⋅ exp( − X ) = Y , assuming: [ X ,Y ] = 0.

(22)

Because the identity matrix commutes well with all other matrices, the identity matrix [1] multiplied by an arbitrarily large coefficient C is added and subtracted: T

(

)⋅ + C ⋅ [1] − C ⋅ [1]) ⋅ exp ( −IJ [ K ] [ M ] ) dt.

R = Δ ⋅ ³ [ M11 ] exp −t [ K c ][ M11 ]

(

−1

0

⋅ { I c } ⋅ [ M11 ]

−1

−1

−1

c

11

The components in above integral can be separated as follows:

(23)

68

K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition

( ) ⋅ exp ( LA) ⋅ exp ( −IJ [ K ][ M ] ) dt − − Δ ⋅ ³ [ M ] exp ( −t [ K ] [ M ] ) ⋅ C ⋅ [1] ⋅ ⋅ exp (t [ K ][ M ] ) ⋅ exp ( −T [ K ] [ M ] ) dt, T

R = Δ ⋅ ³ [ M11 ] exp −t [ K c ] [ M11 ] −1

−1

−1

c

0

T

0

−1

−1

11

c

11

−1

c

11

11

(

(24)

−1

c

11

)

where: LA = ln {I c } ⋅ [ M11 ] + C ⋅ [1] . −1

Now, the exponents in above formula can be disentangled and integrated:

( (

)

(

R = T ⋅ [ M11 ] ⋅ Δ ⋅ exp −T [ K c ][ M11 ] + LA − C ⋅ exp -T [ K c ][ M11 ] −1

−1

−1

)).

(25)

This formula allows to calculate sensitivity components for the right-hand side of sensitivity equation (17).

10. Recognition of conductivity distribution The dependence of measurement coil (shown in Figs. 4, 5) voltage on the variation of electric conductivity γ inside finite elements is represented by the sensitivity matrix [S(t)] for consecutive time steps i :

ª V (t1 ) º ª S1 (t1 ) S2 (t1 ) S3 (t1 ) «V (t ) » « S (t ) S (t ) S (t ) 2 2 3 2 2 » « 1 2 « « V (t3 ) » = « S1 (t3 ) S2 (t3 ) S3 (t3 ) « » « .... .... « .... » « .... «¬ V (ti ) »¼ «¬ S1 (ti ) S2 (ti ) S3 (ti ) with :

.... S j (t1 ) º ª Δγ 1 º .... S j (t2 ) » « Δγ 2 » » » « .... S j (t3 ) » . « Δγ 3 » » » « .... .... » « .... » .... S j (ti ) »¼ «¬ Δγ j »¼

(26)

j - number of finite elements in the search region, i - number of time steps of electromagnetic field evaluation.

The terms of sensitivity matrix are derived from sensitivity equation (17). V means the differences between the measured and actually simulated coil voltage. Solving (26) as linear equations system the corrections to conductivity in finite elements Ȗ are obtained. It can be called quasi-Gauss-Newton algorithm. The process is non-linear and must be repeated iteratively. In the case of poor convergence truncated singular value decomposition of the sensitivity matrix is applied, as described in [1]. The process starts with initial configuration, in our case with a conductivity distribution without cracks. The search regions were applied with number of elements j lower then the number of time steps i, so the equations system (26) was overdetermined. The excitation current had the shape of unit-step, so the solution (8) was exploited. After each iteration the conductivity in search region was corrected with Ȗ. For the next iteration the sensitivity S was evaluated anew. When the coil moves over the crack, number of equations i consists of number of time steps multiplied by the number of coil positions (10 steps in examples below).

K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition

69

The examples below (Figs. 4, 5) show conductivity distribution inside tube wall estimated after 15 iterations. The input data for assumed crack shape were taken not from measurement, but from simulation utilizing the FEM-model with coarser discretization. It gave the similar effect as a presence of noise provided by real measurement. The original flaw had non-zero conductivity of Ȗ = 0,1[MS/m]. The size of test flaws is shown in Figs.4 and 5. The solutions were carried out using modified vector potential u = A·r and cylindrical symmetry.

Figure 4. Rectangular flaw shape and conductivity distribution obtained after 15 iterations.

Figure 5. Skew flaw and conductivity distribution obtained after 15 iterations.

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K.M. Gawrylczyk / Semi-Discrete Time-Domain Sensitivity Analysis for Cracks Recognition

Conclusions The drawback of numerical identification of flaws basing on sensitivity analysis is high computation cost. Comparison of the semi-discrete method efficiency to classical FETS shows, that despite of high demand for memory, the described method may compete in relation to finite elements with the time stepping. Although in this work only two-dimensional examples are presented, conclusions drawn above are directly applicable to solution of three-dimensional models. The results of sensitivity evaluation using semi-discrete method were validated comparing it to usual finite elements with time stepping. We obtained good convergence for simulated voltages of measurement coil. It has to be pointed, that the convergence of numerical identification algorithm described in this paper depends strongly on precise measurement of coil voltage (it’s time function). The measurement has been simulated using finite element model with coarse discretization. In the case of application of real measurement data the convergence of identification process would be worse. In future works the described method will be combined with space mapping technique, described in [5] and successfully applied to defect characterization in [6].

References [1] K. M. Gawrylczyk, M. Kugler, Time domain sensitivity analysis of electromagnetic quantities utilizing FEM for the identification of material conductivity distributions, COMPEL, 25 (2006), 589 598. [2] K. M. Gawrylczyk, M. Kugler, Semi discrete time domain sensitivity analysis of electromagnetic field, COMPEL, 28 (2009), 1138 1348. [3] R. Sridhar, R. Jagannathan, On the q analogues of the Zassenhaus formula for disentangling exponential operators, Journal of Computational and Applied Mathematics 160 (2003), 297 305. [4] D. N. Dyck, D. A. Lowther, E. M. Freeman, A Method of Computing the Sensitivity of Electromagnetic Quantities to Changes in Materials and Sources, IEEE Transactions on Magnetics, Vol. 30, No. 5 (1994), 3415 3418. [5] J. W. Bandler, Q. S. Cheng, S. A. Dakroury, A. S. Mohamed, M. H. Bakr, K. Madsen, J. Sondergaard, Space mapping: the state of the art, IEEE Transactions on Microwave Theory and Techniques, vol.52, 1 (2004), 337 361. [6] R. K. Amineh, S. Koziel, N. K. Nikolova, J. W. Bandler, J. P. Reilly, A space mapping methodology for defect characterization from magnetic flux leakage measurement, IEEE Transactions on magnetics, vol 44, 8 (2008), 2058 2065.

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-71

71

Metamodel as Input of an Optimization Algorithm for Solving an Inverse Eddy-Current Testing Problem Rémi DOUVENOT a,1 , Marc LAMBERT a and Dominique LESSELIER a a Département de Recherche en Électromagnétisme, Laboratoire des Signaux et Systèmes UMR 8506 (CNRS - SUPELEC - Univ Paris-Sud), 91192 Gif-sur-Yvette, France Abstract A method to characterize defects by processing eddy current testing (ECT) signals is presented. It works in a short time for generic defects and work pieces. To retrieve the dimensions of a defect, a metamodel based Particle Swarm Optimization (PSO) is considered. Indeed, using a metamodel as an input of a stochastic method enables to significantly speed it up. The metamodel is generated using an adaptive database generation. Both tube and plate configurations, corre sponding with either simulated or laboratory controlled measured data are consid ered as illustration. Good accuracy and satisfactory speed of the method are exhib ited, additional information besides the inversion results being provided as well, which highlights possibly indeterminate cases, making the method useful also for decision analysis. Keywords. Eddy current testing, Metamodel based inversion, Particle swarm optimization, Decision analysis

Introduction Eddy-current testing (ECT) is a well-known non-destructive technique for defect detection in metal parts. Yet ECT signals can be used also to characterize a defect, beyond mere detection. In the framework of the present study, a (quasi-)real-time method is aimed at. This implies that there is strong a priori information about the tested workpiece and the type of defects to be characterized. Previous efforts to reach this goal have focused on learning algorithms, with encouraging results as seen in [1,2]. To improve the learning step, adaptive databases have been introduced [3]. Here, the adaptive databases are employed to create a metamodel, which is used as an input of a Particle Swarm Optimization (PSO). A fast stochastic inverse method is then obtained. It is put to the test on a number of cases, involving synthetically generated data and laboratory-controlled measured data, in both tube and plate configurations. To create the metamodel, an adaptive database is generated, refer to [4]. This database in practice concentrates a higher number of points where the output variations are the fastest ones, with respect to those of the inputs. In so doing, all the variations of 1 Corresponding

author e mail: [email protected]

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R. Douvenot et al. / Metamodel as Input of an Optimization Algorithm

the outputs with relatively few points can be encompassed. This being made, a classical radial basis function (RBF) interpolation [5] with a thin plate spline kernel function is applied. The adaptive database interpolated by RBF is the metamodel that is used to feed the stochastic inverse method. The performances of the metamodel-based inversion method are illustrated for two configurations, each corresponding to one benchmark: a circular tube workpiece affected by groove defects (two parameters are to be retrieved) and a plate with parallelepiped defects (three parameters are to be retrieved). For each configuration, the method is applied on many simulated signals and a couple of measured data extracted from the benchmarks.

1. The metamodel-based PSO method 1.1. Forward problem solver Let us assume that tests are performed on generic pieces. Constitutive materials and geometrical dimensions of both workpieces and probes are known, at a given frequency of operation. The input parameters are the ones describing the defect inside the workpiece. Then the response of the flawed piece to the probe is computed via an integral volume formulation (see for example [6]), and a variation of impedance is obtained as an output. The CIVA simulation software [7] is used for this purpose. If P are the input parameters and y is the measured or simulated output impedance, we denote y = L(P). Other methods could obviously be preferred for carrying out the forward simulations. For our purpose, the forward simulations are only used to generate the database. 1.2. Generation of the adaptive database The aim of the adaptive database is to get, at the end, input parameter sets with equivalent simulated output impedance variations, which are such that there exists a higher density of inputs where the output variations are faster. The database is created iteratively in order to achieve this goal. This adaptive database generation is described in some more detail in [4]. First, a coarse mesh is generated. Then, at each edge of each simplex of the mesh, simulations are compared to linearly interpolated data. If the interpolation error ε, defined below, is larger than a prescribed stopping criterion, a node is added in the middle of the longest edge of the simplex. An example of a 2D mesh is shown in Figure 1. The interpolation error ε is expressed as ε=

ˆ ||22 ||y − y ||y||22

(1)

ˆ are the exact and the interpolated data, respectively. where y and y Once all calculations have been performed, the database is a set (Pi , yi )i=1,··· ,N where N is the size of the database, each vector P being of dimension D (number of parameters to describe a defect), and each vector y being of dimension M (number of measurement points for one configuration). The generation of the adaptive database certainly is a crucial step for metamodelbased optimization. Depending upon the formulation of the interpolation error, different

R. Douvenot et al. / Metamodel as Input of an Optimization Algorithm

73

Parameter 2

1

00

Parameter 1

1

Figure 1. Example of a 2D adaptive database.

behaviors of the interpolated data can be observed (a better accuracy on low or high amplitude signals for instance) [8]. 1.3. Interpolation of the database The aim of interpolating the database is to create a metamodel. The operator L is approached via an expression depending on the data in the database, this involving little computational effort compared to a forward ECT simulation. Once the database has been created, an RBF interpolation is used to create the metamodel. That is, when an input P is given, the output y can be approximated by the quantity ˆ ˆ = L(P) y =

N 

wi K(P, Pi ),

(2)

i=1

where K is a so-called kernel function, and where the weights wi are computed during a training step. In the following, the thin plate spline kernel function [9], which is commonly used for interpolation, is chosen (Eq. 3). However, other kernels could be preferred without stringent differences being expected. The thin plate spline kernel can be expressed as  K(P1 , P2 ) =

 P2 P1 − P2 22 ln (P1 − P2 2 ) if P1 = 0 if P1 = P2

(3)

1.4. Stochastic optimization The stochastic optimization is carried out by Balanced PSO [10] as a variant of the classical PSO method [11]. It is a metaheuristic based on swarm intelligence. Its principle is that particles moving in the input space while sharing information can find the global minimum. Having an impedance data y (the objective function), particles (usually about 20 [10]) are positioned in the input space with given initial speeds. For each one, a cost function is calculated, and the particles are moved towards likelier positions. The particles share information with some of them (generally 3 or 4) to know which particle has obtained the minimum cost function. Thus, the updated speeds of the particles depend

74

R. Douvenot et al. / Metamodel as Input of an Optimization Algorithm

on their current speeds, weighted by an inertia w, on their best personal position, called personal best p, and on the best position known by the particle, called social best s. At iteration k, and along each dimension d ∈ [1, . . . , D], the positions x of the particles are updated according to the formula: vd (k + 1) = w × vd (k) + r1 c1 (pd (k) − xd (k)) + r2 c2 (sd (k) − xd (k)) xd (k + 1) = xd (k) + vd (k + 1)

(4)

where r1 and r2 are uniformly chosen in [0,1] (independently on each dimension). w, c1 , and c2 are constants chosen following [11] (w = 0.7 or 1, randomly; c1 = c2 ≈ 1.193). The method is known to be relevant for solving nonlinear inverse problems [12], and its balanced version, which is consisting in sending a particle around a local minimum at each iteration, improves the compromise between exploration of the input space and exploitation of the interesting areas [10]. Stochastic methods as PSO are expensive since they require many simulations of the forward problem. With a metamodel to replace the simulation, the cost is significantly reduced and the method becomes relevant in view of almost real-time applications. Yet, consequently, the accuracy of the optimization is directly related to the accuracy of the metamodel. One of the advantages of stochastic methods is also that the many cost function evaluations to be performed can be used in order to localize areas of large likelihood, which is useful to obtain a decision analysis tool.

2. Results on benchmark data Results are discussed for two standard ECT configurations: a tube and a plate. 2.1. Tube workpiece As first configuration, a circular cylindrical non-magnetic tube has been chosen. It is considered of infinite extent along the tube axis. Its internal diameter is 19.68 mm and the wall thickness is 1.27 mm. The test probe is made of a 70-wrapping emitting bobbin of internal diameter 15.66 mm, thickness 0.67 mm, and length 2 mm, and of an identical receiving bobbin which is placed at 0.5 mm of the emitting one. The impedance variation is collected on a distance of 19 mm. This configuration is extracted from the 2008 ECT benchmark that is discussed in [13]. To successfuly apply the presented inversion method, strong a priori information is required. Here, the defect is assumed as being a circular notch with varying length and depth. Its depth is taken between 10 and 90 % of the wall thickness, and its length is taken between 0.1 and 10 mm. The defect can either open at the internal surface or the external surface of the tube. First, two databases are generated, one database per type of defect. Then, two metamodels are generated. The inversion method is tested on 400 test cases randomly selected (defect parameters) and synthetically generated (impedance variations): 200 internal defects and 200 external defects. A metamodel-based PSO inversion is carried out on each generated impedance variation. The inverted parameters are the likeliest ones obtained with this inversion. The type of defect (internal or external) is assumed to be known, and

75

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80

70

70

60

60

Depth (%)

100 - Depth (%)

R. Douvenot et al. / Metamodel as Input of an Optimization Algorithm

50 40 30

PSO likelihood PSO parameters True parameters

20 10

2

4

6

Length (mm) (a) GE40

8

50 40 30 20 10

2

4

6

Length (mm)

8

(b) GI10

Figure 2. Results of the metamodel based PSO inversion on measured data GE40 and GI10.

the inverse problem reduces to a regression on two continuous parameters. The normalized quadratic error q = (Pd − Pˆd )2 /Pd2 is computed for each test case and is averaged on the 200 test cases. For the internal defects, the average normalized quadratic error q¯ is 1.5 % for the depth and 1.9 % for the length. For the external ducts, the error q¯ is 0.6 % for the depth and 0.5 % for the length. Since the metamodel is used as the input of the optimization algorithm, these results are obtained in less than 2 seconds on a 3 GHz personal computer. Two specific results are detailed. They are results on real data corresponding to this configuration and given in [13]. Measurements are avaiable for two defects: GE40 is an external defect with a 40 % depth, and GI10 is an internal defect with a 10 % depth. Both have the same length of 1 mm. Figure 2 shows the results on these two sets of measured data. Darker areas correspond to the likeliest parameter values, the lighter ones to less likely parameter values. The approximation of the likelihood is obtained using the computations carried out during the inversion. The circles correspond with the true parameters of the defects, and the squares give the likeliest ones retrieved by PSO. The approximation of the likelihood gives all the sets of parameters for which the signal due to the reconstructed defect is close to the measured one (the darkest area). Since different defects can lead to similar signals, comparing the measured signal with the one due to the more likely defect is not relevant for the purpose of making a decision analysis tool. The results obtained by the metamodel-based PSO inversion with this configuration appear very good in a reasonable time. The result obtained on GI10 is particularly promising because it is a very low signal, harder to invert. Comparisons of this method with support vector machines on this data can be found in [8]. 2.2. Slab workpiece As second configuration, a non-magnetic plate workpiece is considered, from the COFREND benchmark [14]. Its width and length are considered infinite, and its thickness is 1.55 mm. The probe is a 328-wrapping bobbin of internal diameter 2 mm, thick-

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100 - Depth (%)

100 - Depth (%)

80 60 40 20 0

60 40 20

5

10 Length (mm)

0

15

0.2

0.4 0.6 Width (mm)

0.8

1

0.2

0.4 0.6 Width (mm)

0.8

1

14

Figure 3. Results of the metamodel based PSO inver sion on measured data F5 (depth 100 %, length 2 mm, and width 0.1 mm).

Length (mm)

12 PSO likelihood PSO parameters True parameters

10 8 6 4 2

ness 1.25 mm, and length 2 mm. The probe scans a 8 mm per 12 mm surface. The defect position is assumed to be known, at the center of the scanned zone. The defect is a rectangular notch with varying length, width, and depth. Its depth is considered between 10 and 100 % of the tube thickness, its length is taken between 0.5 and 15 mm, and its width between 0.1 and 1 mm. The average normalized quadratic error q¯ is 0.6 % for the depth, 1.0 % for the width, and 3.2 % for the length of the defect. These results are obtained with an average time of 5.5 s on the same computer as in section 2.1. So, in general, the accuracy of the inversion is good. Two measurements corresponding to this benchmark have been processed. F5 corresponds to a defect of depth 100 %, length 2 mm, and width 0.1 mm. F7 corresponds to a defect of depth 40 %, length 10 mm, and width 0.1 mm. The two inverted results are displayed in Figures 3 and 4, respectively. Both results are quite similar: the inverted parameters are acceptable yet not perfectly retrieved. However, the true parameters are inside the likeliest areas. In particular, it is difficult to precisely decide upon the depth of crack F5 or upon the width of the crack F7. These examples show how undetermined cases can be identified by the inversion method. If other inversions were to be carried out on the same data, and since a stochastic inversion is non repeatable, slightly different results could be found (minimum of the cost function). However, the likeliest area should be approximately the same. So, the inversion tool is appropriate for decision analysis.

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100 - Depth (%)

100 - Depth (%)

80 60 40 20 0

60 40 20

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0

15

0.2

0.4 0.6 Width (mm)

0.8

1

0.2

0.4 0.6 Width (mm)

0.8

1

14

Figure 4. Results of the metamodel based PSO inver sion on measured data F7 (depth 40 %, length 10 mm, and width 0.1 mm).

Length (mm)

12 PSO likelihood PSO parameters True parameters

10 8 6 4 2

3. Conclusion A metamodel-based optimization as a means to perform defect characterization by processing ECT signals has been presented. Interesting results on both simulated and measured data have been shown. This method requires strong a priori information (workpiece and global shape of the defect), but it can be applied to various problems. Defects in a tube and a plate have been retrieved successfully. Moreover, the time necessary to invert the data is reasonable and rather promising for on-site use. Let us note that this tool is also able to retrieve the local minima of the cost function, which makes it suited to decision analysis. A representation of the data in a lower dimensional space (by principal component analysis for instance) could speed up the RBF interpolation. More forward simulations could then be performed in the stochastic method and the inversion could be improved. Indeed, the more time devoted to the stochastic inversion, the more accurate the inversion. But, the true challenge is to apply this type of methods to problems involving, say, 5 input parameters or more. Indeed, as the dimension is increased, the generation of an accurate database requires more and more forward simulations, possibly far too many for realistic use. In this case, other means in metamodel generations should be considered [15].

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Acknowledgements The authors thank CEA (Commissariat à l’Énergie Atomique) and the COFREND working group “Eddy current modelization” for providing the measured benchmark data.

References [1] [2]

[3] [4] [5] [6] [7] [8]

[9] [10] [11] [12] [13]

[14] [15]

L. Udpa and S. Udpa. Eddy current defect characterization using neural networks. Mater. Eval., 48:342 347, 1990. A. Bernieri, L. Ferrigno, M. Laracca, and M. Molinara. Crack shape reconstruction in eddy current testing using machine learning systems for regression. IEEE Trans. Instrum. Meas., 57:1958 1968, 2008. J. Pávó and S. Gyimóthy. Adaptive inversion database for electromagnetic nondestructive evaluation. NDT & E Int., 40:192 202, April 2007. G. Franceschini, M. Lambert, and D. Lesselier. Generation of adaptive database results synthesis. Technical report, Laboratoire des Signaux et Systèmes, January 2009. M. D. Buhmann. Radial Basis Functions: Theory and Implementation. Cambridge University Press, Cambridge, 2003. J. R. Bowler, S. A. Jenkins, Sabbagh L. D., and Sabbagh H. A. Eddy current probe impedance due to volumetric flaw. J. Appl. Phys., 75:8128 8137, 1991. CIVA: State of the art simulation platform for NDE. available at http://www civa.cea.fr, accessed the 8th of June 2010. R. Douvenot, M. Lambert, and D. Lesselier. Particle optimization with metamodel for crack character ization. In Proceedings of the 2010 URSI Electromagnetic Theory Symposium (EMTS 2010), 2010. 4 pp., to appear. F. L. Bookstein. Principal warps: Thin Plate Splines and the decomposition of deformations. IEEE Trans. Pattern Anal. Mach. Intell., 11:567 585, 1989. M. Clerc. The mythical balance or when Particle Swarm Optimisation does not exploit. Unpublished, 6 pp., available at http://clerc.maurice.free.fr/pso/Balanced_PSO/Balanced_PSO.pdf, 2008. M. Clerc. Particle Swarm Optimization. ISTE, London, 2006. P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa. Evolutionary optimization as applied to inverse scattering problems. Inverse Problems, 25:123003, 2009. 41pp. C. Reboud, G. Pichenot, and S. Mahaut. 2008 ECT benchmark results: Modeling with CIVA of 3D flaws responses in planar and cylindrical workpieces. In 35th Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE - 2008), Chicago, 20 25 july 2008. 8 pp. COFREND benchmark. available at http://www.cofrend.com/modelisationcf/GT_CF_COFREND_ GB. html, accessed the 8th of June 2010. R. R. Barton. Simulation optimization using metamodels. In Proceedings of the 2009 Winter Simulation Conference, pages 230 238, Austin, TX, December 13 16 2009.

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Fast Multipole Method for 3D Electromagnetic Boundary Integral Equations. Application to Non Destructive Testing on Complex 3D Geometries Tekoing LIM a Gregoire PICHENOT a and Marc BONNET b a CEA-List, 91191 Gif-sur-Yvette, France b LMS, Ecole Polytechnique, 91120 Palaiseau, France Abstract. The motivation of this work is to develop a computational treatment of eddy current simulation applicable to complex 3D geometries. To this end, an approach based on surface integral equations and involving the homogeneous fullspace Green’s function and dyad is developed. A Galerkin variant of the method of moments, using bilinear basis functions, is employed for discretizing the surface integral equations, leading to a linear system. Solving the linear system using a direct matrix solver is prohibitively expensive in computing time and memory resources. This difficulty is circumvented by using an iterative solver (typically GMRES) together with the Fast Multipole Method (FMM). The response of an eddy current probe is finally expressed with the Auld reciprocity theorem. Keywords. Fast Multipole Method, Surface Integral Equations, Method of Moments, Singularity

Introduction The response of an eddy current probe can currently be modelled in the CIVA non destructive testing (NDT) simulation platform (www-civa.cea.fr) by eddy current technique (ECT) simulation for planar and cylindrical geometries. The developed ECT simulation models are mainly based on the volume integral method using the dyadic Green formalism, for which semi-analytical representations are known for canonical geometries. The motivation of this work is to develop a treatment addressing complex 3D geometries (see Figure 1(a)), which responds to real industrial interest. It aims at modelling the response of an eddy current probe on complex, homogeneous and non-magnetic 3D geometries affected by a flaw (see Figure 1(b)).

1. The proposed approach As a semi-analytical representation of the Green dyadic is unknown for complex 3D geometries, an alternative approach is developed. This approach involves the homogeneous

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T. Lim et al. / Fast Multipole Method for 3D Electromagnetic Boundary Integral Equations

(a)

(b)

Figure 1. (a) Imaginary part of the surface density current J for f = 105 Hz and σ = 106 S/m (results for 1062 edges) and (b) a complex 3D geometry affected by a flaw.

full-space Green function gki (r, r ) and dyad Gki (r, r ) where ki is the wavenumber in vacuum (i = 0) or in the medium (i = 1). It is based on transmission conditions on the surface of the object S given by n0 × E0 = −n1 × E1

and

n0 × H0 = −n1 × H1

on S,

(1)

where a field A is read A0 in vacuum, A1 in the medium (n1 = −n0 is the normal on S oriented toward the medium). Moreover it is convenient to decompose fields into their incident and scattered parts according to Ai − Ainc = Ascat on S. i i

(2)

Let M(r) and J(r) be the surface magnetic and electric densities of current defined by M(r) = M1 (r) = −n1 × E1 (r)

and

J(r) = J1 (r) = n1 × H1 (r),

the electric and magnetic scattered fields are given on S by the integral formulations  1 (r) = × M (r) + ∇ gki (r, r ) × Mi (r )dr n Escat i i i 2 S  −jk0 Gki (r, r ) · Ji (r )dr S  (3) 1 Hscat (r) = Ji (r) × ni − ∇ gki (r, r ) × Ji (r )dr i 2 S  i − jk0 Gki (r, r ) · Mi (r )dr μi S with the Green function 

e+jki |r−r | gki (r, r ) = , 4π|r − r | 

and the Green dyad

T. Lim et al. / Fast Multipole Method for 3D Electromagnetic Boundary Integral Equations

81

Figure 2. Surface discretization

Gki (r, r ) = [I +

1 ∇∇]gki (r, r ). ki2

We then insert (2) and (3) in the transmission conditions (1), and solve the problem for M and J by employing a Galerkin variant of the method of moments [1]. 1.1. Surface discritization A surface discretization with bilinear quadrilateral finite elements is used (see Figure 2). The surface currents are expressed as: 

Nquad

M(r) 

Mq (rq )

q=1

where Mq is the value corresponding to the q-th quadrilateral and Nquad the number of quadrilateral on S. On each element, the surface currents are expressed as: Mq (rq ) =

4 

q Mm fm (rq (u, v))

m=1 q where Mm are the current values corresponding to the m-th local edge of each element and fm (rq ) are the basis functions described as

1 (1 + u)aqu (u, v) JSq 1 f2 (rq (u, v)) = q (1 − u)aqu (u, v) JS 1 q f3 (r (u, v)) = q (1 + v)aqv (u, v) JS 1 q f4 (r (u, v)) = q (1 − v)aqv (u, v), JS f1 (rq (u, v)) =

au (u, v) and av (u, v) are units vectors expressed as

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T. Lim et al. / Fast Multipole Method for 3D Electromagnetic Boundary Integral Equations

au (u, v) =

∂r(u, v) , ∂u

av (u, v) =

∂r(u, v) , ∂v

and where the surface Jacobian JS (u, v) is given by JS = |au × av |. 1.2. Solving the linear system A Galerkin variant of the method of moments, using bilinear basis functions, is employed for discretizing the surface integral equations, leading to the linear system, with matrix Z and primary field Minc (r) and Jinc (r).

Z

M · J



bM = bJ

(4)

Accurate 3D simulations of eddy currents may lead to a matrix Z of huge size (higher than the capacity of a standard PC). Consequently, solving the linear system using a direct matrix solver is prohibitively expensive in computing time and memory resources. This difficulty is circumvented with the use of an iterative solver (typically GMRES) to find the surface currents M(r) and J(r) by minimizing     

Z

M · J



  bM  − J  b 

with the use of the Fast Multipole Method (FMM) [2], which accelerates the computation of products of the matrix Z with the surface currents [M(r) , J(r)] and which avoid the explicit evaluation of the matrix Z. The response of an eddy current probe is finally expressed with the Auld reciprocity theorem, which involves the electric current M(r) and the magnetic current J(r). The FMM has been generally used for problems with dielectric objects without attenuation. In this work, we are dealing with low frequency electromagnetic problem and conductive regions, which are typical conditions under which ECT are applied, for the application of FMM.

2. Fast Multipole Method 2.1. FMM algorithm The FMM is based on the subdivision of the region of space containing S into cubic clusters. The double integrals arising from the Galerkin discretization are then divided into near interactions (involving pairs of adjacent clusters) and far interactions (involving pairs of non-adjacent clusters). The former are computed using classic integral equation methods, while the latter are computed using a multipole expansion of gk1 (r, r ) and Gk1 (r, r ). On the basis of preliminary numerical tests, it has been found that the most suitable FMM formulation in the medium (k1 ) for ECT application is the decomposition in diagonal form given by

T. Lim et al. / Fast Multipole Method for 3D Electromagnetic Boundary Integral Equations

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Figure 3. Fast Multipole principle

g(r, r ) =

e−jk1 R −jk1 = 4πR 16π 2

 |s|=1

−−→ −→ −−→ e−jk1 s·Or T L (s, O O)e−jk1 s·r O ds,

(5)

where R = |r − r |, O and O are the centers of two non-adjacent clusters and the −−→ transfer function T L (s, O O) is defined in terms of the Legendre polynomials Pl and the spherical Hankel functions of the first kind hl by  −−→ −−→ (1)  O)  (2l + 1)j l hl (−k1 |O O|)Pl (s · O T L (s, O O) =

(6)

0≤l≤L

2.1.1. Far clusters The interactions between two clusters are schematically depicted in Figure 3. Starting from the source cluster centered at O , the information on each source’s element r are concentrated at O by the operator F (r O ). Then informations defined at O are transferred to the center O using the transfer function T L (s, O O). Finally, F (Or) dispatches informations from O to each element r in the observation cluster centered at O. 2.1.2. Near clusters As the FMM is not valid for adjacent clusters, computation of the interactions in this case need to be done explicitly. We need to pay attention of the singular behaviour of Green’s function involved in the treatment of near interactions. The Green function has a singularity for r = r . But this divergence disappears while integrating the Green function on the surface of the object, which is properly managed with adapted methods. The Green function is first split into a singular part and a regular part like 1 gk1 (r, r ) = +   4πR 

singular part



 k12 jk13 2 jk1 k14 3 + + R− R − R + ··· . 4π 2!4π 3!4π 4!4π    regular part

(7)

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Table 1. Gain of computation time of FMM’s LF/HF compared to the explicit calculation for different values of the wavenumber used in NDT applications k = 525+525j

k = 1664+1664j

k = 3441+3441j

k = 5256+5256j

FMM LF

50 x faster

8 x faster

-

-

FMM HF

50 x faster

20 x faster

10 x faster

4 x faster

The regular part is integrated using classical methods and integrations involving the singular part are performed using Duffy transformations [3]. 2.2. Most suitable multipole expansion for NDT Different multipole expansions exist, called High Frequency (HF) or diagonal form, and Low Frequency (LF). As low frequency occurs in NDT applications, one might think that the LF expansion is the most suitable multipole expansion. However, FMM has been generally used for problems with a real wavenumber (dielectric object without attenuation) whereas problems involve a complex wavenumber in NDT applications, due to the conductivity of the object. Preliminary numerical tests have been done to evaluate computing time with explicit calculation and FMM’s HF/LF in NDT. Comparison of computation time is shown for two far clusters with 100 elements in each one. So 10,000 interactions have to be computed in explicit calculation and 201 interactions for FMM. Even if less interactions is needed with FMM, the time spent to calculate the integration in Equation 5 has to be evaluated to compare the methods. One can remark in Table 1 that the gain of computation time of FMM LF compared to the explicit calculation is only significant for low value of wavenumber. On the other hand, the gain of computation time of FMM HF is significant for almost all values of wavenumber involved in NDT applications. So even if in NDT applications, we are dealing with low frequency electromagnetic problem, the most suitable multipole expansion for NDT is the expansion called HF (in the medium). It is possible to explain theoretically this result by analysing the wavenumber expression with and without attenuation. • wavenumber expression with attenuation: |k 2 | = |ω 2 μ0 (0 + jσ/ω)| ≈ ωμ0 σ • wavenumber expression without attenuation: k 2 = ω 2 μ0  0 For example, in NDT applications using low frequency, for σ = 0.7 MS/m and f = 100kHz, we have |k 2 | = 5.5 × 105 . But in comparison, without attenuation, we need f = 35GHz to get the same value of |k 2 |. That’s why HF expansion is the most suitable multipole expansion for NDT (low frequency electromagnetic problem but with conductive regions). A first study has been done to define the conditions under which the calculation FMM works properly in the NDT applications. For example, figure 4 shows the accuracy of the FMM HF expansion as a function of the truncation level L and the integer Q (such that the integration over the unit sphere appearing in (5) is effected using (Q + 1)(2Q + 1) quadrature points),

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85

Figure 4. Accuracy of the FMM HF expansion based on L and Q for k1 = 1662 + 1662jm−1 and centers of far clusters distance of 2a with a = 10−2 m

for k1 = 1662 + 1662jm−1 and centers of far clusters distance of 2a with a = 10−2 m. The recommended truncation level is Lopt = 0.55(real(L) + imag(L)) √ √ with L = 3k1 a + 7.5 log10 ( 3k1 a + π), with Q then chosen as Qopt = 1.5Lopt .

3. Preliminary Validation Tests Preliminary tests have been done on planar geometries (see Figure 5) and curved geometries (see Figure 6 depicting the computed distribution of the current density J on a cylindrical sample). The response of an eddy current probe in the presence of a complex object affected or not by a flaw, leads to the computation of the variation of impedance ΔZ of the probe in the presence of the object: Z = Z0 + ΔZ, where Z0 is the impedance of the probe in free space (i.e. in the absence of the object).

Figure 5. Configuration for the validation tests on planar geometries

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Figure 6. Computed distribution of current density J on a cylindrical sample

For canonical geometries, for example a plate, it is possible to calculate this variation of impedance with the Dodd and Deeds approach [4] or by using the Auld reciprocity theorem [5] once the linear system (4) is solved for J and M:  I 2 ΔZ = − J · E0 − M · H0 ds. (8) S

The equivalence of the two approaches has been numericaly checked by expressing surface currents J and M and primary field E0 and H0 on the surface of the object with Dodd and Deeds calculation. Therefore, Equation 8 can be used since the linear system (Equation 4) has been resolved. Conclusion and perspectives In this paper, we report a modelling study aiming at simulating the response of an eddy current probe on complex, homogeneous and non-magnetic 3D geometry affected by a flaw. The Galerkin variant of the method of moments is employed for the surface integral equations with bilinear basis functions to solve the linear system (Eq. 4) by using an iterative solver together with the Fast Multipole Method. Preliminary validation tests have been done on planar geometries. Numerical validations on canonical geometries are in progress by comparison with CIVA’s results. Ongoing work concerns also the extension of the approach in order to take into account a contrast of conductivity inside the defect. References B. C. Usner, K. Sertel, M. A. Carr and J. L. Volakis, Generalized Volume-Surface Integral Equation for Modeling Inhomogeneities With High Contrast Composite Structures, IEEE Trans. Antennas Propag., Vol. 54, No. 1, Jan. 2006 [2] G. Sylvand, La méthode multipôle rapide en électromagnétisme: Performances, Parallélisation, Applications, PhD Student, Ecole Nationale des Ponts et Chaussées, Juin 2002. [3] J. D’Elìa, L. Battaglia and M. A.Storti, Full Nulmerical Quadrature in Galerkin Boundary element methods, CIMEC, INTEC, CONICET, 2008. [4] C.V Dodd, W.E. Deeds and J.W. Luquire, Integral Solutions to some Eddy Current Problems, International Journal of Nondestructive Testing, Vol.1, pp. 29-90, 1969. [5] B.A. Auld, F.G. Muennemann and M. Riaziat, Quantitative Modelling of Flaw Responses in Eddy Current Testing, Nondestructive Testing, Vol. 7, 1984. [1]

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Computation of the magnetostatic field in nonlinear media via the integral equation formalism: Application to the characterization of Magnetic Flux Leakage NDT system Emna Amira FNAIECH a Denis PRÉMEL a,1 , Claude MARCHAND b and Bernard BISIAUX c a CEA, LIST, Laboratoire Simulation et Modélisation, PC 120, F-91191, Gif sur Yvette Cédex, France b Laboratoire de Génie Electrique de Paris (LGEP), CNRS-Supélec (UMR 8507), Gif-sur-Yvette, France c VRA - Vallourec Research Aulnoye, Aulnoye-Aymeries, France Abstract. This paper deals with the development of a fast numerical semianalytical model dedicated to the simulation of the non-destructive testing of ferromagnetic tubes by using the magnetic flux leakage method(MFL). Taking into account the characteristic of the ferromagnetic material, the B-H curve, the numerical model is based on the generalized boundary element method which implies the evaluation of two magnetic fictitious scalar densities. Integral equations are discretized via the Galerkin’s method and the particularity of this paper lies in the implementation of high order basis functions for the interpolation of the scalar unknowns. Simulated data provided by the numerical model are compared to FE data in order to show the validity of the numerical approach. Keywords. NDT by magnetic flux leakage, Magnetostatic regime, Nonlinear media, Galerkin’s method, High order basis functions.

Introduction The detection of flaws in steel pipes by using the magnetic flux leakage technique consists in magnetizing the pipe and due to the presence of a defect, a fraction of the flux lines leaks from the pipe’s wall in the air inside or outside the pipe. This leakage flux is detected by a magnetic sensor or an induction coil. In the Vallourec group, a world leader manufacturer of steel pipes, most of NDT units use MFL for testing ferromagnetic pipes. In order to improve the performances of flaw detection, specifically for inner flaws, the CEA LIST and the Vallourec Research Aulnoye (VRA) are aiming to develop 1 Corresponding

Author: Denis Prémel, CEA LIST; E-mail: [email protected]

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a fast 3D numerical model for the simulation of MFL systems. In a first step, the framework addresses an experimental system specifically dedicated to the detection of longitudinal flaws. A simplified 2D geometry derived from the second magnetic MFL benchmark problem proposed by the World Federation of NDE centers [1] has been previously studied [2] considering a linear regime. This means that at low magnetization, the ferromagnetic material behaves like a linear material. In this case, the semi-analytical model based on the boundary element method (BEM) has been implemented and numerically validated. This preliminary work could give satisfaction for linear model but we truly aim to improve the capabilities of detection for different kinds of defects. For the detection of external defect, a low level of magnetization is usually sufficient but in order to detect an inner defect or buried defects, we have observed that it is preferable to increase significantly the level of magnetization [2]. In this case, the main difficulty in the computation of the magnetostatic field within the pipe of ferromagnetic material lies in the nonlinearity of the B-H curve characterizing the material constituting the magnetizing circuit and the pipe. Each material can also be characterized by its own specific B-H curve. The framework of this present work consists in extending the first semi-analytical model for computing the magnetostatic field in the pipe considering the non-linear regime. For solving a non-linear magnetostatic problem, the generalized boundary element method (BEMG) is widely used since the statement of the problem is determined by two equivalent scalar potentials: the surface charge density and the volume charge density [3,4,5]. This numerical approach has the capability to compute the response of an arbitrary defect in the pipe. Nevertheless, this paper is focused on the numerical validation of the semi-analytical model in the non-linear regime and without any flaw.

1. Integral Equation Formalism Let us consider some finite domain occupying a finite volume V , bounded by a surface S and made of a ferromagnetic material. The non-linear problem is considered: the B-H curve associated to the material is introduced in the model. μr (r) stands for the relative permeability. Some encircling coils generate a source magnetic field Hs which can be calculated by using Biot-Savart law [6]. The total magnetic field is splitted into the sum of the source field and the unknown induced field produced by ferromagnetic regions: H(r) = Hs (r) + Hi (r). The total field is related to the magnetization vector M(r) = (μr − 1) H(r). The resolution of the modeling problem amounts to determine the induced field Hi (r) produced by fictitious magnetic sources. The estimation of the surface and volume magnetic charges is performed by using the extended boundary element method implying boundary (surface in 3D) elements and surface (volume in 3D) elements. This approach is briefly described in the following section. The development, based on Maxwell’s equations and satisfying the condition ∇ · B = 0, leads to a system of two equations combining a surface integral equation and a volume integral equation [4]. The forward problem consists in evaluating two scalar functions: the surface charge density σ denoted by σ(r) = M(r) · n(r) and the volume charge density ρ denoted by ρ(r) = −∇ · M(r). When solving the non-linear case, the surface charge density does not vary significantly compared to the linear case, so the convergence of the iterative process cannot be reached. To overcome this problem, it is necessary to solve the forward problem in two steps. The first one consists in assuming

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that the magnetic permeability is infinite in such a way that the volume charges density disappears. In this case, the surface charge density denoted by σ∞ must be computed as follows:  1 σ∞ (r) + ∂n G(r, r ) σ∞ (r ) ds = −n(r) · Hs (r) (1) 2 S with the normal vector n(r) pointing outwards from the volume V , G(r, r ) denotes the Green’s function in the free space and ∂n G is defined by ∂n G(r, r ) = n(r)·∇G(r, r ). Then, in the non-linear case, we consider that the total surface charge density σ results from the addition of σ∞ (r) and a correction term δσ such as: σ(r) = σ∞ (r) + δσ(r)

(2)

A new system of two coupled integral equations leads to the computation of the difference surface charge δσ and the volume charges density ρ:  δσ(r) + ∂n G(r, r ) δσ(r ) ds + 2λ(r) S  λ(r) − 1 σ∞ (r) ∂n G(r, r )ρ(r ) dτ = (3) 2λ(r) V  ∇G(r, r )(δσ(r ) + σ∞ (r )) ds + ρ(r) + ∇ln(μr (r)) · S

 ∇ln(μr (r)) ·

V

∇G(r, r ) ρ(r ) dτ = −∇lnμr (r) · Hs (r)

λ is defined by λ(r) =  Hi (r) =

S

μr (r)−1 μr (r)+1 .

(4)

Then, the total induced magnetic field is given by:

∇G(r, r ) σ(r ) ds +



∇G(r, r ) ρ(r ) dτ

(5)

V

The two coupled equations (4) and the observation equation (5) need to be discretized in order to solve numerically the forward problem.

2. 2D Implementation and discretization 2.1. Geometric discretization Before starting to solve the 3D problem, we chose to study the 2D model. The first step involves approximating the geometry by an appropriate mesh which leads to the discretization of the integral equations. Each contour of the piece is divided into curvilinear elements and each surface is approximated by a number of quadrilateral elements (with 8 or 9 nodes). So, the coordinates of any point on each curvilinear segment (quadrilateral element) are defined from the coordinates of the nodes using the shape functions:

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x=

n 

xi Ni (ξ),

y=

i=1

x=

nq 

xi Ni (ξ, η),

n 

yi Ni (ξ)

for curvilinear elements

(6)

for quadrilateral elements

(7)

i=1

y=

i=1

nq 

yi Ni (ξ, η)

i=1

where Ni (ξ), Nqi (ξ) are the shape functions usually used in Finite Element Methods. n and nq are respectively the number of nodes associated to each curvilinear element and to each quadrilateral element. 2.2. The choice of basis functions The unknowns of the problem, the surface charge density and the volume charge density translated into the 2D problem, are interpolated by using a set of basis functions. Two interpolation techniques are implemented: the first one uses isoparametric elements and the second one is based on higher-order basis functions. 2.2.1. Isoparametric elements The discretization of integral equations by using isoparametric elements involves using similar functions for the approximation of the geometry and for the interpolation of the unknowns. The two unknown scalar functions are expressed as: σ(r) =

n 

σi Ni (ξ),

ρ(r) =

i=1

nq 

ρi Ni (ξ, η)

(8)

i=1

For this description, the number of unknowns σi (ρi ) corresponds to the number of nodes defining the contour (the surface). 2.2.2. Higher-order basis functions The second interpolation technique is based on the use of basis functions of high order. The two unknowns of the problem are expressed in series of Legendre polynomials of higher order whith the following development: σ(r) =

M  m=0

σm Cm Pm (ξ),

ρ(r) =

M q Nq  

ρmn Cm Pm (ξ)Cn Pn (η)

(9)

m=0 n=0

where M , (Mq and Nq ) are respectively the order of Legendre polynomials used for the description of the σ density on an elementary curvilinear element and for the description of the ρ density on one elementary quadrilateral element. Pm (ξ), Pn (η) are respectively the Legendre polynomials and the Legendre polynomials modified [7], Cm and Cn are some scaling factors. The total number of unknowns (the number of coefficients σm ) is equal to (M + 1) × Ne where Ne is the number of curvilinear elements describing the contour of the ferromagnetic region. The number of unknowns (the number of coefficients ρmn ) is equal to (Mq + 1) × (Nq + 1) × Neq where Neq is the number of elements defining the surface of the ferromagnetic domain. These two techniques of interpolation are compared in the following in order to test their efficiency and we expect to reduce the computation time and the memory space with high order basis functions.

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2.3. The matrix system To avoid the difficulty to define the surface charge density at any point of the mesh, we have used the Galerkin method. The matrix system is finally obtained by: 

Aσσ Aσρ Aρσ Aρρ



   δσ b = ρ g

(10)

with A

σσ



 =

fi (r) Γe

σρ

A

fi (r) + 2λ(r)





=

Aρρ =

 Se



 Se

fqi (r)

 g=−

Se

fj (r)∂n G(r, r )dΓk dΓe

(11)

Γk

(12)

fj (r)∇lnμr (r) · ∇G(r, r )dΓk dSe

(13)

Sk

Sk

 fqj (r)∇lnμr (r) · ∇G(r, r )dSk dSe



 fi (r) Γe



Γk

 fqi (r) fqi (r) +

b=



fqj (r)∂n G(r, r )dSk dΓe

fi (r) Γe

Aρσ =



 λ(r) − 1 σ∞ (r)dΓe 2λ(r)

 fqi (r) ∇lnμr (r) · Hs (r) +

(14)

(15)

 σ∞ (r )∇lnμr (r) · ∇G(r, r )dΓk dSe Γk

(16) where f and fq denote respectively the basis functions associated to contours and the basis functions associated to surfaces, e and k denote respectively the indices of the observation element and the source element. If we use isoparametric elements, the shape basis functions fi and fj are associated to the nodes indexed respectively i and j. If we use higher order basis functions, the indexes i and j stand for the order of Legendre polynomial series. Due to the fact that the magnetic relative permeability depends on the local intensity of the magnetic field, this matrix system is solved iteratively. At each iteration, the magnitude of the magnetic field is evaluated in each quadrilateral element considering a number of observation points. Then, the gradient of the logarithm of the magnetic relative permeability is deduced numerically by using spline interpolation functions.

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3. Numerical validation 3.1. System The implemented numerical model can be firstly validated by considering a simplified geometry without any geometric corner. Let us consider a ferromagnetic pipe which is magnetized by two coils driven by a constant current. The material of the tube being ferromagnetic, the B-H curve of the ST37 steel, represented in Figure 1(b), has been introduced into the iterative process. A 2D view of this simplified geometry is displayed in Figure 1(a). The geometry is assumed to be infinite along the transverse axis perpendicular to the plane of the figure. Two kinds of simulated experiments are conducted. For

(a) System studied

(b) Tube ST37

Figure 1. Configuration and ferromagnetic material used

the first one, we aim to validate the numerical results provided by the semi-analytical model and other simulated ones obtained by using a finite element software. The second numerical experiment aims at highlighting the interest of the use of higher order basis functions rather than the use of shape basis functions of second order. 3.2. A comparison between IEM - FEM data The mesh of the tube contains a total number of elements equal to Neq = 200. The inner radius of the tube is Rin = 48 mm and the outer radius of the tube is Rout = 88 mm. The current density driving the two coils is fixed at Js = 1.1 105 A/m2 . This level of magnetization allows one to go beyond the linear part of the B-H curve. Keep in mind that in this numerical experiment, the unknown scalar functions are interpolated by using isoparametric elements. The radial component and the tangential component of the magnetic field are computed on a circumferential line, outside the tube with a distance of 2 mm from the outer surface. The angle of each computation point varies from 45◦ to 135◦ . All simulated data are compared in Figure 2(a) and 2(b). Figure 3(a) displays a cartography of the intensity of the magnetic flux density inside the tube. Figure 3(b) extracts some specific values on a radial line at θ = −60◦ from R = 47.5 mm to R = 87.5 mm. The good agreement between simulated data shows the numerical validity of the semi-analytical proposed model. In the following, we look for the improvement of the accuracy of the numerical model by using higher order basis functions.

E.A. Fnaiech et al. / Computation of the Magnetostatic Field in Nonlinear Media

(a) Hr

93

(b) Hθ

Figure 2. The radial and the tangential components of the magnetic field provided by FEM and IEM.

(a) A cartography of |B|

(b) An extracted radial line at θ = −60◦

Figure 3. Magnitude of the magnetic flux density inside the tube.

3.3. The interest of higher-order basis functions In any geometry which contains a geometric corner, we expect to observe very huge variations of the field at the vicinity of the corner [8]. In such a situation, it is required to refine the mesh around the corner but in this case, the number of unknowns can grow up strongly. This seems to be very harmful for the computational time and the memory space. In order to give a better approximation of theses variations, we preferably choose to use higher order basis functions, keeping in mind that the geometry remains well approximated with a coarse mesh. In order to show the interest in the increasing of order, a coarse mesh with Neq = 75 is applied for both interpolations techniques (shape functions of second order and high order functions). Some reference numerical results are nevertheless obtained with a fine mesh with shape functions of second order. Figure 4(a) and Figure 4(b) show the radial and the tangential components of the magnetic field along a radial line inside the tube and located at θ = −60◦ . These numerical results show really the interest of high order basis function. Indeed, this interpolation method provides better capabilities for representing the local variations of the field without the need of a refine mesh.

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(a) Hr

(b) Hθ

Figure 4. The radial and the tangential components of the magnetic field: A comparison between numerical results obtained by shape functions of second order and by higher order basis functions.

4. Conclusions and perspectives This paper is focused on the development of a 2D numerical model for solving a specific non-linear magnetostatic problem dedicated to NDT MFL systems. First numerical results show a good agreement between IE data provided by the semi-analytical model and FE data. Two semi analytical numerical models based on two different techniques of interpolation have been implemented. Thus, the advantage of using high order basis functions is clearly illustrated. It seems to be necessary to build up a fine mesh for approximating with a good accuracy the complex geometry and to ensure a good evaluation of the unknown scalar densities, implicitly the intensity of the magnetic field, it is interesting to obtain a better description of the unknowns with high order basis functions. Thanks to this numerical approach, any B-H curve can be introduced since we solve the non linear problem by an iterative procedure. In order to pursue this work, specific numerical problems due to numerical singularities remain to overcome. Moreover, we hope to give a better approximation of more complex geometries without using a fine mesh but by using Non-Uniform Rational Basis Splines NURBS. In close future work, we aim to simulate the second magnetic MFL benchmark problem, a specific NDT system proposed by the World Federation of NDE centers [1].

References [1] Z. Zeng, Y. Tian and S. Udpa, "Finite Element Modeling of the World Federation’s Second MFL Benchmark Problem", Review of Progress in Quantitative Nondestructive Evaluation, 23(700), (2004), 1553– 1559. [2] EA. Fnaiech, D. Prémel, C. Marchand and B. Bisiaux, "A fast numerical model for predicting magnetic flux leakage signals due to defects in a steel pipe by using an integral equation approach", Proceedings of the 8th International Symposium on Electric and Magnetic Fields (EMF2009) [3] B. Krstajic, Z. Andelic, S. Milojkovic, S. Babic, and S. Salon, "Nonlinear 3D magnetostatic field calculation by the integral equation method with surface and volume magnetic charges". IEEE Transactions on Magnetics, 28(2), (1992),1088–1091. [4] W. Hafla, A. Buchau, F. Groh and W.M. Rucker, "Efficient integral equation method for the solution of 3D Magnetostatic problems". IEEE Transactions on Magnetics, 41, (2005), 1408–1411. [5] J. McWhirter, J. Oravec, and R. Haack, "Computation of magnetostatic fields in three-dimensions based on fredholm integral equations", IEEE Transactions on Magnetics, 18, (1982), 373–378.

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[6] I.R. Ciric, "Surface source models and formulas for the magnetic field of polygonal cross section conductors". IEEE Transactions on Magnetics, 24(6), (1988), 3132–3134. [7] E. Jorgensen, J L. Volakis, P. Meincke, "Higher order hierarchical legendre basis functions for electromagnetic modeling", IEEE Transactions on Antennas and Propagation, 52(11),(2004), 2985–2995. [8] F. Groh, W. Hafla, A. Buchau and W.M. Rucker, "Field strength compuation at edges in nonlinear magnetisatics", The international Journal for Computation and Mathematics in Electrical and Electronic Engineering, 23(3),(2004),662–669.

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-96

Efficient computation of eddy current crack signals Theodoros THEODOULIDIS 1 University of Western Macedonia, Department of Mechanical Engineering, Greece Abstract. In simulations of eddy current inspections using the boundary element method (BEM) is is often the case that the calculation of the system matrix carries the largest computational cost. This matrix calculation typically makes use of a Green’s function expressed as a Fourier integral. The present study has aimed to reduce the computational cost by adopting an alternative approach for the rapid computation of the Green’s function in the spatial domain. This is possible by employing Sommerfeld integral expressions and by approximating them in terms of discrete complex images. Theoretical results are compared to both benchmark experimental data for a semi-elliptical crack and to numerical data from a finite element commercial package. Agreement is excellent over a wide frequency range. Keywords. Eddy current testing, crack modelling, Sommerfeld Integrals, Discrete Complex Image Method, Boundary Element Method

Introduction In the application of the Volume Integral Method (VIM) for the simulation of eddy current defect inspections we employ the following integral equation for the calculation of the electric field in the presence of a void defect embedded in a multilayered conductive half-space [1]  E(r) = E(0) (r) + iωμ0 G(r|r ) · p(r )dr (1) V0

where E(r) is the electric field with the defect present, E(0) (r) is the electric field with the defect absent (incident field), G(r|r ) is the electric-electric dyadic Green’s function defined as the field response to a unit point source (electric dipole), p(r ) is the unknown electric dipole density, V0 is the defect volume and primed and non-primed position vectors refer to source and field points respectively. When, however, the defect has the form of a crack, the very narrow crack opening can make the use of (1) somewhat problematic because a dense discretization is required across the gap in order to get accurate results. The situation is even worse in the limit of a vanishing gap which describes the ideal crack case, when the crack is represented by just a surface impenetrable to the eddy current flow. In such a case of a narrow or ideal 1 Corresponding Author: Theodoros Theodoulidis, University of Western Macedonia, Department of Mechanical Engineering, Bakola & Sialvera, 50100 Kozani, Greece; E-mail: [email protected].

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crack, instead of using (1), we can replace it with a simpler integral equation if we take into account the very fact that at the crack surface the normal component of the eddy current density vanishes. After imposing this condition we obtain [2]  Jn(0) (r± ) = −k 2 Gnn (r± |r )p(r )dS  (2) S0

where S0 is the crack surface and subscript n denotes the direction normal to the crack surface. Since the discretization of the crack is reduced from a volume to a surface, the BEM is used instead of VIM. The model based on the solution of (2) has been recently developed to achieve high computational efficiency. In [3], where a literature review of research work regarding the model is presented, further improvements are suggested on the original numerical scheme in [2] regarding computation of the incident field, Green’s function computation and singularity treatment. In [4], an alternative approach is suggested for the Green’s functions computation and for the simulation of cracks with shapes other than rectangular. During all these developments, the computation of the Green’s function, i.e. the Green’s function matrix fill time was identified as the bottleneck in the calculations. In the present work, we study the subject from a different perspective and compute these functions in the spatial domain. This is possible by employing the Discrete Complex Image Method (DCIM) which in turn is based on the efficient evaluation of the Sommerfeld integrals. The method employs the Generalized Pencil of Function (GPOF) method to approximate the Sommerfeld integral expression for the kernel with a series of complex exponential functions and hence cast them in closed form [5], [6]. This is similar to the method presented in [4] but with a basic difference that will be explained later. Results are provided for a semi-elliptical crack and they are compared to benchmark experimental results. The same configuration is also modelled with a numerical method (a 3D-FEM commercial package) in order to identify the differences between the two methods.

1. Green’s function Consider Figure 1 which shows a cylindrical coil above a narrow slot in a homogeneous conductive and non-magnetic half-space. The coil is excited by a time harmonic current varying as the real part of I exp(−iωt). The crack surface is discretized in small rectangular elements and a constant dipole density is assumed over each element. The constant dipole density is equivalent to representing the dipole distribution with pulse functions. The integral equation is then transformed to a linear system of equations by imposing the vanishing current constraint at the middle points of the elements, which is the definition of point matching and is equivalent to the use of delta functions as testing functions. The solution of the integral equation (2) yields the dipole density on the crack surface, which acts as a secondary eddy current source. This source determines the coil impedance due to the crack. By using a reciprocity relation, we can calculate directly the crack signal (impedance change due to the crack) through [2]  1 ΔZ = 2 Jx(0) p dV0 (3) I σ V0

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T. Theodoulidis / Efficient Computation of Eddy Current Crack Signals

z Coil y Δx O

x

Crack

Figure 1. Coil above a narrow crack in a conductive half-space.

where σ is the half-space conductivity. In this paper we are interested in the calculation of the term Gxx used in (2) by finding the x-component of the electric field produced in the half-space by an elementary electric dipole oriented also in the x-direction. The Green’s function consists of two parts. (r) Gxx = G(s) xx + Gxx

(4)

(s)

(r)

where Gxx is the part that arises in the unbounded space and Gxx is the part arising from the air-conductor interface. The calculation of (4) has to be done for each combination of source and field cells that comprise the grid of the discretized crack. Hence, in each case Gxx accounts for the interaction between the cells. The source part is given directly in the spatial domain by 

∂ 2 eikR 2 G(s) = k + (5) xx ∂x2 4πR  (x − x )2 + (y − y  )2 + (z − z  )2 , while the expression for the xwith R = component of the reflected electric field produced by an electric dipole, in Cartesian coordinates, is as follows [3], [7] G(r) xx

1 = 4π 2

∞ ∞ −∞ −∞



eλ(z+z ) κ2 λ

   2 2λ− κ 2 2 k v − u λ ei[u(x−x )+v(y−y )] dudv (6) λ+κ

√ √ with κ = u2 + v 2 and λ = κ2 − k 2 . Both expressions (5) and (6) have to be integrated over the source volume, i.e. over x , y  , z  to determine the matrix used in finding a numerical solution. The advantage of (6) is that it allows analytical integration over the source cell dimensions but it has the disadvantage that a double improper integral has to be computed for each matrix element. The method proposed in [3] was to approximate (6) by Fourier series.

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T. Theodoulidis / Efficient Computation of Eddy Current Crack Signals

1.1. Discrete Complex Image Method Nevertheless, an extensive search in the literature of Green’s function computations shows that it can be computed rapidly and accurately in the spatial domain. In this case we use a cylindrical coordinate system (ρ, ϕ, z) centered on the field point and express (r) Gxx in the following form [3], [7], which uses Sommerfeld type integrals. G(r) xx

k2 = 4π

∞

0

cos2 ϕ + 4π

λ−κ1 λ+κλ

∞

0





eλ(z+z ) κJ0 (κρ) dκ

κ2 − 2κλ λ

sin2 ϕ − cos2 ϕ + 4πρ

∞

0





eλ(z+z ) κJ0 (κρ) dκ

κ2 − 2κλ λ





eλ(z+z ) J1 (κρ) dκ

(7)

where Jn denotes the n order Bessel function. Eq.(7) has to be integrated over the source cell volume. In particular, the integration over the z-dimension of the source cell, i.e. over z  , can be done analytically. Assuming a cell of Δz extent we obtain 

 G(r) xx dz

k2 = 2π

∞  0

cos2 ϕ + 2π

λ−κ1 sinh λ+κλ

∞  0



λΔz 2

κ2 − 2κλ sinh λ

sin2 ϕ − cos2 ϕ + 2πρ

∞  0





 κ eλ(z+z ) J0 (κρ) dκ λ

λΔz 2



κ2 − 2κλ sinh λ

 κ eλ(z+z ) J0 (κρ) dκ λ



λΔz 2

 eλ(z+z



)

(8)

1 J1 (κρ) dκ λ

Now we seek an analytical calculation of the above integrals. For that we utilize the following identities ∞ 0

∞ 0

κ λz eikR e J0 (κρ) dκ = λ R 1 λz eikR − e−ikz e J1 (κρ) dκ = λ ikρ

(9)

(10)

with z ≤ 0. By approximating the bracketed terms with exponentials of the complex variable λ  

λ−κ1 λΔz = c1,n es1,n λ (11) sinh λ+κλ 2 n

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T. Theodoulidis / Efficient Computation of Eddy Current Crack Signals

κ2 − 2κλ sinh λ



λΔz 2

 =



c2,n es2,n λ

(12)

n

we end up with a closed form expression for the reflected part of the Green’s function  eikR1,n eikR2,n k2  cos2 ϕ   G(r) c1,n + c2,n xx dz ≈ 2π n R1,n 2π R2,n n +

eikR2,n − e−ikz2,n sin2 ϕ − cos2 ϕ  c2,n 2πρ ikρ n

(13)

! 2 . The reason for calling the method where zj,n = z + z  + sj,n and Rj,n = ρ2 + zj,n Discrete Complex Image is now obvious. The Green’s function consists of images located at a complex distance Rj,n (compare to (5)). Eq.(13) has to be integrated over the x and y-directions. This can be done numerically or even analytically if first the term eikR2,n /Rn is Taylor expanded as an m-th degree polynomial in Rn . Such an approach is followed in [8] and leads to considerable time saving. The error introduced with such an expansion is given by a closed-form expression depending on the approximating polynomial degree and the ratio of the cell dimensions and thus it is controlled by the number of terms in the Taylor series. In our case, having set x = y = 0 (field point  at the center of the cylindrical coordinate system), we make the substitution ρ = x 2 + y  2 and ϕ = arctan (y  /x ) and integrate numerically (13) in order to obtain Gxx for (2). The approximation in (11)-(12) is possible with the GPOF algorithm [5]. Note that the algorithm has to be performed in each equation just once since it does not depend on the specific distance between the source and the field cells. In [4], the GPOF algorithm was used for approximating the Sommerfeld integral kernel with exponentials of the real κ variable. Such an approach results in an expression that can be evaluated analytically over the volume of the source cell but it requires multiple GPOFs for each z + z  combinations. This is the basic difference of the present approach and the one in [4].

2. Results Here we present results for a benchmark problem described in [9]. A coil is moved above and along a semi-elliptical crack and the impedance change due to the crack (real and imaginary part) is recorded with respect to the coil position. The semi-elliptical notch has length 22.1 mm, max depth 8.61 mm and width 0.33 mm. The host material is Aluminum with conductivity 22.5 MS/m. The cylindrical coil has inner radius 2.51 mm, outer radius 7.38 mm, height 4.99 mm, 4000 wire-turns and lift-off 0.491mm. The signals are presented for 16 frequencies that cover a wide range from the very low to the very high. In order to present them all in a common diagram, they are all normalized to the isolated coil inductive reactance X0 = ωL0 with a theoretical value of L0 =100.47 mH and an experimental one L0 =100.45 mH. The term low and high frequency is defined by the crack depth to skin depth ratio. For example at 50 kHz this ratio is 18.15 and the case is defined as a thin-skin limit case or a high frequency case. Fig.2 compares the normalized complex impedance plane crack signals obtained from the BEM model to experimental data and also to numerical results from a 3D-FEM

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T. Theodoulidis / Efficient Computation of Eddy Current Crack Signals

0.035

0.03

f [Hz] 250 356 507 721 1027 1462 2081 2963 4218 6006 8550 12172 17329 24670 35121 50000

0.025

ΔX/X

0

0.02

0.015

0.01

0.005

0

−0.005 −0.02

−0.015

−0.01

−0.005 ΔR/X

0

0.005

0.01

0

Figure 2. Impedance plane crack signals for the 16 frequencies shown on the right of the diagram. Comparison of theoretical BEM (lines) to experimental (dots) and FEM (circles) results.

calculation [10]. Excellent agreement is observed at all frequencies. Computation time was about 11 hours for the FEM (31 coil positions and 16 frequencies from 250 Hz to 50 kHz) and 20 seconds for the BEM with a quad-core I7 processor, 16 GB memory computer. Computation times for the different parts of the calculation were provided in [4]. The computation time for FEM increases linearly with the coil positions in contrast to BEM where the time does not depend on this factor. The BEM computation time on the other hand depends on the frequency since higher frequencies require a denser grid for the discretized crack. For the FEM the same grid was used for every frequency with good results.

3. Conclusions We have presented a method for rapidly computing the Green’s function matrix, which is the slowest part in the computation of crack signals via method of moments. Impedance predictions compare very well to experimental measurements as well as to FEM calcu-

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lations. There are many ways to further extend the scope of the model. For example, it can incorporate various coil types or coils under conditions of tilt [11], since their effect enters through only the incident field.

Acknowledgements The work is funded by CEA LIST in the framework of the collaborative project CIVAMONT 2012.

References [1]

[2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

S. Paillard, G. Pichenot., M. Lambert and H. Voillaume, Eddy current modelling for inspection of riveted structures in aeronautics, Electromagnetic Nondestructive Evaluation (X), S. Takahashi and H. Kikuchi (Eds.), IOS Press, (2007), 25–32. J.R. Bowler, Eddy current interaction with an ideal crack. I. The forward problem, J. Appl. Phys. 75 (1994), 8128–8137. T. Theodoulidis, N. Poulakis and A. Dragogias, Rapid computation of eddy current signals from narrow cracks, NDT&E Int. 43 (2010), 13–19. T. Theodoulidis, Developments in efficiently modelling eddy current testing of narrow cracks, NDT&E Int. 43 (2010), 591–598. Xing Lingling, Rapid calculation of eddy current field Green’s function using the matrix pencil method, NDT&E Int. 42 (2009), 85–91. M.I. Aksun, A robust approach for the derivation of closed-form Green’s functions, IEEE Trans. Microwave Theory and Techniques 44 (1996), 651–658. A. Banos, A dipole radiation in the presence of a conducting half space, Pergamon Press, 1966. L. Alatan, M.I. Aksun, K. Mahadevan and M.T. Birand, Analytical evaluation of the MoM matrix elements, IEEE Trans. Microwave Theory and Techniques 44 (1996), 519–525. D.J. Harrison, L.D. Jones and S.K. Burke, Benchmark problems for defect size and shape determination in eddy-current nondestructive evaluation, J. NDE 15 (1996), 21–34. Comsol 3.5a User’s Guide, 2009. T.P. Theodoulidis and E.E. Kriezis, Eddy current canonical problems (with applications to nondestructive evaluation, TechScience Press, 2006.

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-103

103

Experimental Validation of a Fast Non-Iterative Imaging Algorithm for Eddy Current Tomography Salvatore VENTREa, Flavio CALVANOb, Guglielmo RUBINACCIb and Antonello TAMBURRINOa,1 a b

Ass. EURATOM/ENEA/CREATE, DAEIMI, Università di Cassino, Italy Ass. EURATOM/ENEA/CREATE, DIEL, Università di Napoli Federico II, Italy

Abstract. In this work for the first time we validate experimentally a fast (real time) non iterative imaging method for eddy current tomography of conductive materials. The presented method is based on the monotonicity principle applied in the low frequency limit where the skin depth is great with respect to the relevant dimension of the problem under test. The experimental tests prove the effectiveness of the monotonicity based imaging method. Moreover, we prove that the inversion can be carried out without resorting the direct problem solver.

Keywords. Eddy currents, non iterative imaging algorithms, non destructive evaluation, monotonicity, ECT signal inversions.

Introduction In eddy-current testing a prescribed time-varying current flowing in the excitation coils induces eddy currents in the conductive specimen under inspection. The electrical resistivity of the specimen affects the induced eddy currents density and, consequently, the voltage at the receptive coils. The measured data consist of measurements of the impedance matrix (self and mutual impedances) between the coils of the array. In recent years, numerical methods for solving the forward or direct problem, i.e.,

Figure 1. The planar surface to be investigated (specimen) together with a probe made by an array of seven coils and a rectangular defect. 1 Corresponding Author: Ass. EURATOM/ENEA/CREATE, DAEIMI, Università di Cassino, v. G. Di Biasio, 43 Cassino 03043 Italy; e mail: [email protected].

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the problem of predicting the measured quantities for a given electrical resistivity and source current, have been extensively studied. The main applications of the direct problem are: (i) the computer aided prediction of the performances of existing probes, (ii) the design of ad-hoc optimized probes and (iii) the solution of the inverse problem through model based inversion methods. Numerical formulations based on finite element method have been studied and developed by the authors for both volumetric [1] and zero thickness inclusions [2]. A key role in eddy current tomography is the reconstruction of the resistivity profile of the specimen under test, starting from the measurement data, through the solution of an inverse problem. The identification of the conductivity distribution inside a material is seriously affected by the inherently ill-posed and nonlinear nature of the eddy currents inverse problem (see [3]-[5] for mathematical issues). First and foremost, the ill-posedness translates into low sensitivity measurements, i.e. different resistivity distributions produce similar measurements and, in addition, the nonlinearity requires sophisticated inversion algorithms. The imaging methods can be divided in iterative and non-iterative (direct). Usually the iterative algorithms are based on the Gauss-Newton method. Among the iterative methods it is worth mentioning quadratic and higher order approximation of the forward operator, deterministic and stochastic algorithms, pre-calculated database, statistical methods, Total Variation regularization, Level Set regularization, etc. (see [6]-[24] and references therein). As main drawbacks, the iterative methods require the solution of the direct problem for several assigned tentative shapes of the inclusion and this can be very expensive in terms of computational cost. Moreover, the convergence cannot be guaranteed. On the other hand non-iterative methods have attracted a lot of interest because they provide a test for evaluating if a point of the domain (or a subregion) is part or not of the anomaly, regardless other points (or subregions). The test is very cheap from the computational viewpoint because no iterations are necessary. In this paper we present the first experimental validation of the fast and noniterative method based on the monotonicity property of the real part of the measured impedance matrix. This method was initially developed by the authors for elliptic problems such as electrical resistance tomography [25], and later extended to parabolic problems such as the eddy current testing in both low frequency (large skin depth) [26] and high frequency (skin depth negligible with respect to the relevant dimension) [2728]. Numerical simulations of the direct problem have been exploited to check numerically if a given probe was able to guarantee appropriate reconstructions. The monotonicity imaging method has been applied to identify the resistivity profile of several benchmarks. The paper is organized as follows. The monotonicity is proven for a proper unknown-data mapping in Sections 1, the inversion method is presented in Section 2, an experimental validation of the monotonicity imaging method is presented in Section 3 and finally in Section 4 the conclusions are drawn. 1. Monotonicity principle In this section we briefly describe the monotonicity principle for the real part of the measured impedance matrix (self and mutual impedances between pairs of coils of

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the array shown in figure 1). In the low frequency limit, the impedance matrix admits the following expansion: 2 (2) 3 (3) 4 Zcoil (1) D = R0 + jωL0 + Ȧ PD + jȦ PD + O(Ȧ ) that is valid as long as the frequency is enough low so that the 4th and higher order terms in (1) are negligible. We mention that all matrices appearing in (1) are real and symmetric. Matrix PD(2 ) , which contributes to the real part of the impedance matrix, plays a key role because of its monotonicity property [26]. In particular it is possible to show that if the resistivity of the considered material increases pointwise, then the ohmic power dissipated in the conductor decreases and consequently PD(2 ) decreases in the sense that will be clarified in the following. For two-phase materials the monotonicity can be stated as [26]:

V1 ⊆ V2 in D Ÿ PV(2 ) ≥ PV(22 )

(2)

1

where Vk ⊆ D represents the domain occupied by the k-th anomaly (resistivity η a ) that is hosted in the background material having resistivity η b < η a . In (2) PV(12 ) ≥ PV(22 )

means that matrix PV(12 ) − PV(22 ) is positive semi-definite, i.e. all its eigenvalues are nonnegative. 2. Monotonicity imaging method Equation (2) forms the basis for the method to solve the inverse problem (see [26]). Let V be the (unknown) subset of D where the resistivity is ηa (the resistivity in D\V is ηb). The inverse problem consists in retrieving V. Let us consider a generic (and known) test domain k. From (2) it follows that:

PΩ(2) ≥ PD(2 ) false Ÿ Ωk ⊄ D ,

(3)

k

and, thus, by checking (3) for different test anomalies k it is possible to estimate/retrieve V. It is worth noting that the algorithm can be applied to an arbitrary number of anomalies with unknown shape and topology.

Figure 2. The conductive domain D subdivided in elementary regions together with an anomaly V (grey pixels) and a test region Ωk (black pixel).

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S. Ventre et al. / Experimental Validation of a Fast Non-Iterative Imaging Algorithm (2 )

In order to test (3) we need to compute the eigenvalues of PΩ(2k) − PD for checking if this symmetric matrix is positive semi-definite or not. However, only a noisy version ~ PD(2 ) = PD(2 ) + E , PD(2 ) being the noiseless matrix and E the noise matrix, can be measured and it can be processed as described in [26]. Similarly, the test matrices PΩ(2k) may be affected by either measurement errors (if measured) or numerical errors (if ~ ~ (2 ) numerically computed). Therefore, the eigenvalues of PΩ(2k) − PD can be different from the eigenvalues of PΩ(2k) − PD

(2 )

and this may alter in an unpredictable way the sign

of the eigenvalues with smaller magnitude, i.e. this may alter the reconstruction. ~ ~ (2 ) In order to deal with this situation, we quantify how much the matrix PΩ(2k) − PD is positive semi-definite through the so-called sign index sk defined as: M

s k =ˆ

¦λ j =1

k, j

M

¦ λk , j

(4)

j =1

~ ~ (2 ) where λ k , j is the j-th eigenvalues of the matrix PΩ(2k) − PD and M is the number of the available eigenvalues. We notice that sk is closer to 1 when almost all relevant ~ ~ (2 ) eigenvalues are non-negative (sk=1 when PΩ(2k) − PD is rigorously positive semidefinite). In addition, from perturbation theory [29], it follows that the eigenvalues that may change their sign due to the presence of noise, are only those having a magnitude smaller than the Euclidean norm of the noise. When the magnitude of the noise is known or estimated, these eigenvalues can be removed from the summations in (4). Finally, we highlight that the dimension (number of rows and columns) of the ~ ~ (2 ) matrix PΩ(2k) − PD is small because it is equal to the number of coils of the array that, usually, is made by few elements (few tens). Therefore, a very low computational cost (2 ) (computation of the eigenvalues of PΩ(2k) − PD ) is required to compute (4) for performing test (3).

3. Experimental results The experimental tests we describe in the following consist of an array made by two coils mounted in a fully automated imaging system composed by a scanning system, a LCR meter and a PC controlling the whole acquisition and inversion process (figure 3). The specimen under test is a printed circuit boards (PCB, thickness 1.6mm) presenting copper islands , having different size and shapes, to be imaged. The copper islands (thickness 35mm) are union of 5mm×5mm elementary domains. These elementary domains are taken as the k during the imaging process. The sensor, that has been designed through extensive numerical simulations, is made by two pancake coils. The first coil (internal diameter=5mm, external diameter=10.5mm, height=6.5mm, number of turns=700) contains internally the

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second coil (internal diameter=1mm, external diameter=4mm, height=3mm, number of turns=180). Simulated inversions have provided that this array gives no reconstruction errors for a noise level not greater than 50 mΩ. This threshold has been achieved during the experimental test that, therefore, provide error-free reconstructions. The excitation frequency is 30kHz, chosen to satisfy the condition of 4th and higher order terms in (1) negligible. At same time, this frequency guarantees an appropriate magnitude of the measured signal and a noise level smaller than the 50 mΩ threshold. The monotonicity algorithm processes the experimental data providing the reconstruction, in 0.1ms per pixel. It is worth noting that the second order moment for a test domain ( PΩ(2k) ) has been experimentally measured on a 5mm×5mm copper island. Moreover, thanks to the translational invariance of the problem, it has been sufficient to perform the measurement of PΩ(2k) only for a single test domain located on the top side and for a ~ single test domain located on the bottom side. The related measurements are PΩ(2k), bottom ~ and PΩ(2k), top .

3.1. First case The first test is a printed circuit board where the copper forms the letters IP (Inverse Problem) as shown in figure 4 (left). The inversion, that is shown in Figure 4 (right) is error free. This is because the experimental noise level is smaller than the threshold (50 mΩ) found by the aforementioned numerical simulations involving the inversion of synthetic data.

Figure 3. The two coils composing the array (left). The smaller coil is inserted into the bigger one. Block diagram of the measurement system (right).

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Figure 4. The specimen under test (left) and its reconstruction (right). The white pixels represent the conductive pixels. The pixel dimensions are 5mm×5mm.

3.2. Second case The second test is a double-face printed circuit board (see Figure 5). It consists of a double sided PCB (copper, thickness 35μm) as shown in figure 5 (top). The measurements are taken from only the top side of the PCB. In this case the imaging algorithm requires the test domains on both sides on the PCB. The test domains on a side of the PCB provide the reconstruction for the related side. For instance, the test domains on the top side provide an error free reconstruction of the top side (figure 5, left column). On the other hand, the test domain in the bottom layer provide as reconstruction the union of the pixels in the top and bottom sides (figure 5, right column). This unexpected result can be easily explained by considering that it ~ ~ results PΩ(2k), bottom ≤ PΩ(2k), top and, therefore, it is trivial to prove that the test domains related to the bottom side provide a reconstruction that is the union of the pixels from the top and the bottom sides.

4. Conclusions A fast inversion method for inverting eddy-current testing data has been experimentally validated for the first time. Numerical simulation of the whole imaging process (not reported here for the sake of brevity) provide noise level threshold of about 50 mΩ such that for noise level below such threshold the reconstruction is errorfree. The time required to form the image in a single pixel is about 0.1ms. The imaging algorithm is fully non-linear and, therefore, can treat arbitrary shapes and topologies. Moreover, the measured data have been processed by means of pre-measured data and without resorting to the numerical solution of the direct problem that, as well known, is time-consuming.

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Acknowledgements This work was supported in part by the Association EURATOM/ENEA/CREATE, Italy. (a)

(b)

(c)

(d)

Figure 5. The specimen under test: the top side (a) directly under the probe, and the bottom layer (b). Reconstruction obtained by exploiting the test domain located on the top side (c) and reconstruction obtained by using the test domain located on the bottom side (d). For this latter inset the white pixels represent the pixels of the bottom side whereas the grey pixels represent the pixels of the top side.

References [1]

[2] [3] [4] [5]

M. Morozov, G. Rubinacci, A. Tamburrino, and S. Ventre, Numerical Models with Experimental Validation of Volumetric Insulating Defects in Eddy Current Testing, IEEE Trans.on Magnetics, vol. 42, pp. 1568 1576, 2006. R. Albanese, G. Rubinacci, and F. Villone, An integral computational model for defect simulation and detection via eddy currents, J. Comp. Phys., vol.152, pp. 736 755, 1999. D. Colton and L. Paivarinta, The uniqueness of a solution to an inverse scattering problem for electromagnetic waves, Arch. Ration. Mech. Anal., vol. 119, pp. 59 70, 1992. V. Isakov, Uniqueness and stability in multidimensional inverse problems, Inverse Problems, pp. 579 621, 1993. M. Yamamoto, A mathematical aspect of inverse problems for non stationary Maxwell’s equations, Int. J. Appl. Electromagn. Mech., pp. 77 98, 1997.

110

[6] [7] [8] [9] [10] [11] [12] [13]

[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

S. Ventre et al. / Experimental Validation of a Fast Non-Iterative Imaging Algorithm

W. Q. Yang (Guest Editor), Special feature: Electrical Tomography Industrial and Medical, Measurement, Science and Technology, vol. 21, 2001. R. A. Williams and Beck M S (eds), Process Tomography: Principles, Techniques and Applications, Oxford: Butterworth-Heinemann, 1995. M. Soleimani and A. Tamburrino, Shape reconstruction in magnetic induction tomography using multifrequency data, Int. Jour. of Information and System Sciences. vol. 2, pp. 343 353, 2006. W. Yin and A. J. Peyton, A planar EMT system for the detection of faults on thin metallic plates, Measurement Science and Technology vol 17, pp. 2130 2135, 2006. A. Pirani M. Ricci R. Specogna A. Tamburrino and F. Trevisan, Multi frequency identification of defects in conducting media, Inverse Problems, vol. 24, 2008. A. Tamburrino, S. Ventre and G. Rubinacci, Electrical resistance tomography: complementarity and quadratic models, Inverse Problem, vol. 16, pp. 1585 1618, 2000. R. Pierri and A. Tamburrino, On the local minima problem in conductivity imaging via a quadratic approach, Inverse Problems, vol. 13, pp. 1547 68, 1997. G. Rubinacci, A. Tamburrino and S. Ventre, A differential formulation based on a perturbative approach to solve the ECT inverse problem, Comput. Methods Appl. Mech. Eng. vol. 169 pp. 407 24, 1999. D. Dos Reis, M. Lambert and D. Lesselier, Non destructive evaluation of 3 D voids in a metal plate, Inverse Problems, vol. 18, pp. 1857 71, 2002. D. Premel and A. Baussard, Eddy current evaluation of three dimensional flaws in flat conductive materials using a Bayesian approach, Inverse Problems, vol. 18, pp. 1873 89, 2002. J. R. Bowler, Thin skin eddy current inversion for the determination of crack shapes, Inverse Problems, vol. 18, pp. 1891 905, 2002. B. Luong and F. Santosa, Quantitative imaging of corrosion in plates by eddy current methods, SIAM J. Appl. Math., vol. 58, pp. 1509 31, 1998. V. Monebhurrun, B. Duchêne and D. Lesselier, Three dimensional inversion of eddy current data for nondestructive evaluation of steam generator tubes, Inverse Problems, vol. 14, pp. 707 24, 1998. Z. Badics, J. Pávó, H. Komatsu, S. Kojima, Y. Matsumoto and K. Aoki, Fast flaw reconstruction from 3D eddy current data, IEEE Trans. Magn., vol. 34, pp. 2823 2828, 1998. Li Yue, L. Udpa and S.S. Udpa, Three dimensional defect reconstruction from eddy current NDE signals using a genetic local search algorithm, IEEE Trans. Magn., vol. 40, pp. 410 417, 2004. W. Yin, S. J. Dickinson and A. J. Peyton, Imaging the continuous conductivity profile within layered metal structures using inductance spectroscopy, IEEE Sensors J., vol 5, pp. 161 166, 2005. S. M. Nair and J. H. Rose, Reconstruction of three dimensional conductivity variations from eddy current (electromagnetic induction) data, Inverse Problems, vol. 6 pp. 1007 30, 1990. O. Dorn and D. Lesselier, Level set methods for inverse scattering some recent developments, Inverse Problems, vol. 25, pp. 67 131. Q. N. Jin, On the iteratively regularized Gauss Newton method for solving nonlinear ill posed problems, Math. Comput., vol. 69, pp. 1603 23, 2000. A. Tamburrino and G. Rubinacci, A new non iterative inversion method for electrical impedance tomography, Inverse Problems, pp. 1809 1829, 2002. A. Tamburrino and G. Rubinacci, Fast Methods for Quantitative Eddy Current Tomography of Conductive Materials, IEEE Trans. Magn., vol. 42, pp. 2017 2028, 2006. G. Rubinacci, A. Tamburrino, S. Ventre, Eddy current imaging of surface breaking defects by using monotonicity based methods, ACES Journal, vol.23, no. 1, pp. 46 52, 2008. A. Tamburrino, S. Ventre, G. Rubinacci, Recent developments of a Monotonicity Imaging Method for Magnetic Induction Tomography, Inverse Problems, vol. 26, no. 7, pp. 074016, 2010. Golub G H and Van Loan C F 1996 Matrix Computations (Johns Hopkins Studies in Mathematical) Sciences 3rd Edition, Johns Hopkins University Press, Baltimore, USA.

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Numerical Evaluation of Microwave Testing for Pipe Thinning  Yasutomo SAKAI, Noritaka YUSA, Hidetoshi HASIZUME Department of Quantum Science and Energy Engineering, Tohoku University Abstract. This study evaluates the applicability of using microwaves for the inspection of pipe wall thinning by using numerical simulations and experiments. The configuration considered in this study is an axisymmetric one consisting of a straight brass tube and coaxial cables. After the agreement between three-dimensional numerical simulations and experimental result is confirmed, experiments to locate wall thinning are carried out. Clear signals due to the wall thinning are obtained. The time of flight of microwaves agrees with the theoretical prediction, which demonstrates the possibility of locating wall thinning from microwave signals. Key words. Electromagnetic wave, piping detection, wall thinning, FEM

1. Introduction Rapid inspection for piping systems used in chemical or power plants is one of the most important issues from the viewpoint of reducing maintenance costs. Conventional methods such as ultrasonic and eddy current testing provide local information, which results in a long inspection period for large piping systems. Due to this fact, another nondestructive testing method for evaluating a large area at once is highly demanded. Currently, to solve these problems, guided waves are mainly studied[1][2][3]. Guided waves propagate in pipe walls longitudinally, which enables inspection of a broad area. However, there are some problems, such as the reflections at the connections of pipes. Another approach is to utilize microwaves[4][5][6][7]. The basic concept of this method is to regard the pipes as a waveguide and to detect defects from transmission and reflection of microwaves propagating inside the pipes. Since microwaves propagate through the free space surrounded by the metal pipes with little attenuation, connections of pipe do not affect signals so significantly. Recent studies have shown through numerical simulations that the presence of wall thinning affects transmitted energy of microwave, and analyzing the signals in the frequency domain enables one to evaluate the shape of wall thinning[8]. The studies, however, include several problems from the viewpoint of practical applications. That is, the model was quite simplified. In addition, the locations of wall thinning were assumed to be known in advance and only the intensity of the spectrum of measured signals were analyzed. Therefore, the purpose of this study is to evaluate the applicability of microwave nondestructive inspection to the detection and evaluation of wall thinning in more practical configurations. This study conducts three-dimensional numerical simulations and experimental verifications. Obtained signals are analyzed in time domain to correlate the time of flight of the signal with the location of wall thinning.

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2. Materials and Methods The principle of the microwave testing is to evaluate wall thinning from the transmitted and reflected energy of microwave as mentioned above. The time of flight (TOF) of reflection, which is calculated from the group velocity of the microwaves, enables one to locate discontinuities such as wall thinning. Fig. 1 shows the configuration used in both the numerical simulation and the experiment. It consists of a brass tube modeling the piping, and coaxial cables and connectors to inject microwaves into the tube. The coaxial cables are extended into the pipes with a length of 5 mm to suppress the microwave reflections occurring at the end of the cable. Microwaves are generated and the reflected energies are measured at port 1. The microwaves propagate as TEM mode inside the coaxial cables, and are transformed into TE and TM modes inside the tube. This study considered two lengths of a pipe, L=120 and 1120 mm, which are termed as the short and the long range model hereafter. The short range model is evaluated both in numerical simulations and experiments, to confirm the validity of the method as well as to evaluate the behavior of microwaves propagating inside the tube. The long range model is only dealt with by the experiments due to limitations of computational resources needed to consider the model. Table 1 shows the parameters of the two models. The numerical simulations shortened the length of coaxial cables, Lc, into 20 mm to decrease computational resources. The experiment system is composed of semi-rigid cables (K-118 Anritsu), microwave connectors (K-101, Anritsu) several brass pipes and brass plates. The brass plates and the semi-rigid cable are soldered. A short brass tube with a larger diameter is utilized to simulate wall thinnings. That is, actually the brass tube shown in Fig. 1 consists of three tubes connected with flanges. Microwaves are generated and measured by a network analyzer (Agilent PNA, E8363B). Flexible coaxial cables are connected from the network analyzer to semi-rigid cables. Data is obtained in frequency domain and transformed to time domain using inverse Fourier transformation. The numerical simulations are conducted using commercial software COMSOL Multiphysics and its RF Module. The governing equation adopted is

§ σ · ¸E = 0 , rot μ r−1 rotE − k 02 ¨¨ ε r − j ωε 0 ¸¹ ©

(

)

(1)

where

k 0 = ε 0 μ 0ω 2 . 2

(2) Subscript 0 denotes physical quantities in vacuum. Tube wall was modeled as a conductor with a zero thickness and impedance boundary condition,

jωμ 0 μ r

μ0 μr n × H + E − ( E ⋅ n )n = 0 , ε 0ε r − j σ ω

(3)

is imposed on the surface of the tube wall. In the analysis, tetrahedral quadratic vector elements are employed. Table 2 summarizes parameters used in the simulations. It should be noted that the numerical simulations are three-dimensional ones, whereas the configurations are axisymmetric. The cut-off frequencies of TE11, TM01 and TM02 modes in the pipe are 9.25, 12.1, and 19.3 GHz, respectively.



Y. Sakai et al. / Numerical Evaluation of Microwave Testing for Pipe Thinning

113

3. Results Fig. 2 shows comparison of the numerical and experimental results of the amplitude of the reflected energy in the short range model. The figures show good agreement, which



Figure 1 Analysis and experimental system (unit mm)

Table 1 Details of models short range model 120 20(simulation),235(experiment) 40

L[mm] LC[mm] LD[mm]

Table 2 Parameter of Numerical simulations tube wall air 6 0 1 1 1 1

σ[MS/m] μr [-] εr [-]













teflon 0 1 3

$PSOLWXGH> @

$PSOLWXGH> @

long range model 1120 235 290,790





















 )UHTXHQF\>*+]@







 )UHTXHQF\>*+]@

Figure 2. Comparison between simulations (left) and experiments (right)





validates both the simulations and the experiments. The small differences between the two results are mainly caused by the flexible cables not considered in the numerical simulations. Other numerical simulations confirmed that TM01 is dominant inside the pipe, which are not shown in this paper. Fig. 3(a) shows the results of numerical simulations in the short range model. As reflections at the connection part are relatively large, the measured data did not show significant difference. The signals without any defects are subtracted from those

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Y. Sakai et al. / Numerical Evaluation of Microwave Testing for Pipe Thinning

with defects to extract and to evaluate the effect of the defects quantitatively. The subtracted signals are presented in Fig. 3 (b), which shows the reflections caused by wall thinning. Fig. 4 shows the results of experiments in the short range model. The 0.40

0.40 QV

0.30 0.20

0 20 amplitude[-]

amplitude[-]

QV

0.30

0.10 0.00 -0.10

0.10 0.00 -0.10

-0.20

-0 20

-0.30

-0.30

-0.40

-0.40

0.0

1.0

2.0

3.0

0.0

4.0

1.0

time[ns]

2.0

3.0

4.0

time[ns]

(a) Raw data of pipes without wall thinning(right: non wall thinning, left: wall thinning depth 2mm)

0.10

0.54ns

0.10

0.61ns

0.05 amplitude[-]

0.05 amplitude[-]

0.54ns 0.61ns

0.00

0.00

-0.05

-0.05

-0.10

-0.10 0.0

1.0

2.0

3.0

4.0

0.0

1.0

time[ns]

2.0

3.0

4.0

time[ns]

(b) differences(left: depth 2 mm, right: depth 1 mm) Figure 3 Reflected microwaves in the short range model, obtained by the numerical simulations

0.20

2.34ns 2.41ns

0.15

0.15

0.10

0.10 amplitude[-]

amplitude[-]

0.20

0.05 0.00 -0.05

2.34ns

0.05 0.00 -0.05

-0.10

-0.10

-0.15

-0.15

-0.20

2.41ns

-0.20

0.0

1.0

2.0

3.0

time[ns]

4.0

5.0

0.0

1.0

2.0

3.0

4.0

time[ns]

Figure 4 Reflected microwaves in the short range model, obtained by the experiments (left depth 2 mm, right depth 1 mm)

5.0



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Y. Sakai et al. / Numerical Evaluation of Microwave Testing for Pipe Thinning

Table 3 Calculated TOF in short range testing numerical simulation Entrance of pipe 0.23 ns Near edge of wall thinning (25GHz) 0.54 ns Near edge of wall thinning (17GHz) 0.61 ns

experiment 2.03 ns 2.34 ns 2.41 ns

 0.20

0.20 QV

0.15

QV

QV

0.10 amplitude[-]

0.10 amplitude[-]

QV

0.15

0.05 0.00 -0.05

0.05 0.00 -0.05

-0.10

-0.10

-0.15

-0.15 -0.20

-0.20 0

2

4

6

8

10

12

0

2

4

time[ns]

6

8

10

time[ns]

Figure 5 Reflection of wall thinning (LD=290mm, LD=790mm, both depth 2mm) Table 4 Calculated TOF in long range testing 290 mm Entrance of pipe 2.03 ns Near edge of wall thinning (25GHz) 4.25 ns Near edge of wall thinning (17GHz) 4.78 ns

12



790 mm 2.03 ns 8.08 ns 9.52 ns

 signals shown in the figure are also the difference between the models with and without defects. Table 3 shows the calculated TOF of reflections due to the three discontinuities. front edge of wall thinning and the connection part. The TOF of the reflections are evaluated by using the group velocity of two frequencies, 25 and 17 GHz, since the 25 GHz is the maximum frequency considered in the experiment and 17 GHz provides maximum transmitted energy. It should be noted that since the length of coaxial cable of experiment is much longer than that of numerical simulations, TOF of experiment is also larger than that of numerical simulations. Fig. 3(b) and Fig. 4 confirm that the initial rises of measured signals coincide with the TOF of reflections due to the near edge of wall thinning shown in Table 3. These results show the possibility of detecting wall thinning. Signals corresponding to the far edge of wall thinnings are unclear because of the large reflection due to the end of pipe. The results obtained in the short range model also imply that the method would have difficulty in detecting defects located too close to microwave ports.. On the basis of the results above, experiments in the long range model were carried out. The results of the experiments and calculated TOF are shown in Fig. 5 and Table 4, respectively. It should be noted that the signals are not subtracted ones. The strongest signals near 2 ns are the reflection at the connection part. The next signals come from the near edge of wall thinning, and their TOF are between the two TOFs calculated using 25 GHz and 17 GHz, whereas dispersion of the microwaves makes signals unclear. Analyzing modes of electromagnetic waves propagating inside the pipe more quantitatively will lead to more accurate localization of the wall thinning from measured signals.

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Y. Sakai et al. / Numerical Evaluation of Microwave Testing for Pipe Thinning

4. Conclusion In this study, microwave testing for piping systems was evaluated both by three-dimensional finite element simulations and experiments. Signals obtained in frequency domain were converted into time domain to locate wall thinnings from their time of flight. After the validity was confirmed in a short range model, practical experiments using 1120mm long brass pipe were carried out. The results confirmed the validity of the method.

Acknowledgement This work was supported by the Tohoku University Global COE Program on World Center of Education and Research for Trans-disciplinary Flow Dynamics

Reference [1] D. N. Alleyne, M. J. S. Lowe, P. Gawley, The reflection of guided waves from circumferential notches in pipes, Journal of Applied Mechanics 65 (1998), 635-641. [2] P. D. Wilcox, A rapid signal processing technique to remove the effect of dispersion from guided wave signals, Ultrasonics, Ferroelectrics, and Frequency Control 50 (2003), 419-427. [3] Joon-Hyun Lee, Seung-Joon Lee, Application of laser-generated guided wave for evaluation of corrosion in carbon steel pipe, NDT&E International 42 (2009), 222-227. [4] Kavoos Abbasi , Study of Microwave Nondestructive Technique to Detect Crack and Predict Its Location in Piping System, Tohoku University Doctoral Dissertation, (2007). [5] Y. Ju, L. Liu, M. Ishikawa. Quantitative evaluation of wall thinning of metal pipes by microwaves. Materials Science Forum 614 (2009), 111-116. [6] K. Sugawara, Development of inspection method for the defect in pipes using microwave, Tohoku University Master thesis, (2002), (in Japanese) [7] T. Shibata, H Hashizume, S. Kitajima, K. Ogura, Experimental study on NDT method using electromagnetic waves, Journal of Materials Processing Technology 161 (2005), 348-352. [8] Y. Sakai, N. Yusa, S. Ito, H. Hashizume, Numerical analysis of microwave NDT applied to piping inspection, Proceeding of The 13th Asia-pacific Conference on Non-destructive Testing, (2009), 230.

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-117

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Parallelization of Crack Signal Calculation Using CUDA Imre KISS 1 , József PÁVÓ and Szabolcs GYIMÓTHY Budapest University of Technology and Economics, Department of Broadband Infocommunications and Electromagnetic Theory Abstract. A calculation method for the simulation of the Eddy Current Testing (ECT) signal of multiple cracks is implemented on a general purpose video card. NVIDIA’s parallel computing solution, the Compute Unified Device Architecture (CUDA) was used as a shell for the implementation on both hardware and software sides. Possibilities inherent in this technology are shown through an example and a detailed implementation focusing on data parallel execution is discussed. Different realizations of the same algorithm are inspected and a comparison from the view of efficiency is given. Keywords. CUDA, GPGPU, Multiple cracks, Surface integral crack model

Introduction The mathematical model of several different types of defects is given in the form of integral equations. The numerical solutions of such integral equations might be obtained using the Method of Moments. The main computational task in such solutions is the evaluation of the kernel of the integral equation at numerous locations (either spatial or spatial frequency locations) inside the integration domain. Most part of such calculations in a given location can be carried out independently of the calculations related to other locations. Consequently the kernel can be evaluated simultaneously in the desired locations. As a result, parallel computation of this can be easily designed. A number of approaches are known for accelerating an application by parallelizing it. Among others, one may use supercomputers for high performance computing, or could build up a Beowulf cluster from ordinary machines. The application of a target hardware for solving time consuming tasks is also a possibility, like for example the project GRAPE (GRAvity piPE) for n-body computations [6]. It is easy to see that all of these solutions have drawbacks, especially from the financial point of view. In this paper a parallel computing method is described aiming to give an extremely fast evaluation of the signal of a thin crack using a CUDA capable Graphic Processing Unit (GPU). 1 Corresponding Author: Imre Kiss, Budapest University of Technology and Economics, Goldmann György Tér 3, 1111 Budapest, Hungary; E mail: [email protected].

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1. Compute Unified Device Architecture Since graphics hardwares reached notable power, there always have been attempts to use their computational capacity for high-performance computations. One of the main causes preventing the spreading of programs utilizing graphics cards were the complexity how these target devices could be programmed. GPUs were primarily designed for operation on graphical objects, hence long standing programming languages (e.g. OpenGL, DirectX) were hard to be used for solving general, non-graphical related problems. NVIDIA recently introduced its CUDA (Compute Unified Device Architecture) technology [1] which issued in a general purpose graphics hardware. The new design unified the work-flow from shader levels to a general purpose core (the term “unified” is originated here), which serves the needs of both traditional graphical and general purpose utilizations. Consequently, a hardware design consisting of hundreds of processor cores, and capable to execute thousands of threads simultaneously have become available, that can be programmed in a general purpose programming language (a slightly modified version of the regular C language). 1.1. Achievements on parallel computation with CUDA Efforts have already been made at different fields of engineering to utilize gain from the application of GPU based parallel computation. Application fields dealing with large, independent data structures are the primary targets of the utilization. For example in molecular dynamics, the movement of numerous particles perfectly fits into the main idea behind parallelization by treating each particle in a separate thread. In numerical algebra, GEMM routines in the BLAS library give an example on parallel dense matrix multiplication. Many other references could be enumerated from the fields of medical imaging, fluid dynamics, seismic imaging. A good summary on the application fields can be found in [5]. 2. Signal calculation using the multiple thin crack model 2.1. Integral equation model for the calculation of the signal of multiple thin cracks Assume the arrangement shown in Figure 1 where C infinitesimally thin cracks are located close to each other in a conducting specimen. The surfaces and the surface normal vectors of the cracks are Sc and n ˆ c (c = 1, 2, . . . , C), respectively. ECT probe

σ0 , μ0

n ˆ1 n ˆ2

...

n ˆ3 n ˆC

S1 S2 S3 ... SC Surface Cracks Vs : Specimen

Surface Cracks

Figure 1. Eddy current probe above a conductor specimen containing infinitesimally thin planar cracks.

I. Kiss et al. / Parallelization of Crack Signal Calculation Using CUDA

119

The eddy current signal of several infinitesimally thin planar cracks can be calculated by using the extension of the integral equation model of the single thin crack [2]. Each crack is represented by a surface current density pc (c = 1, 2, . . . , C) concentrating on the surface Sc of the crack. The unknown pc functions can be obtained by the solution of the following system of integral equations [3]:

i 0 = Ecn (rc ) −

C  k=1 k=c

 jωμ0 

− jωμ0 lim

 r → rc±

gkc (rc |r  )pk (r  ) dr  −

Sk

gcc (r|r  )pc (r  ) dr  ,

rc ∈ Sc ,

c = 1, 2, . . . , C,

(1)

Sc i (rc ) is the so-called incident field, that is the normal component of the elecwhere Ecn tric field due to the interaction of the probe and the specimen without the presence of ˆ c · Ge (r|r  ) · n ˆ k (k, c = 1, 2, . . . , C), where Ge (r|r  ) is the cracks. gkc (r|r  ) = n the electric-electric Green’s function assuming the geometry of the given specimen. rc± denotes the vector approaching the location vector rc from both sides of the surface Sc . Knowing the solution of (1) the ECT signal, that is the impedance variation of the probe, ΔZ, is calculated as, C  1  i ΔZ = − 2 Ecn (r)pc (r) dr, I c=1

(2)

Sc

where I is the magnitude of the exciting current. 2.2. Discretization of the integral equation In this part we will show that the most time-consuming calculations during the solution of the integral equation (1) can be done parallelly if the method of moments is used for the discretization of (1). For the sake of simplicity assume that the only one crack (C = 1) is located in a plate specimen. The surface of the plate is in the xy plane of the Descartes coordinate system and the crack is in the x = 0 plane (ˆ n1 = xˆ, where xˆ is the unit vector of the x coordinate direction). Assume that the surface current density is approximated by a properly chosen function series as, p1 (y, z) ≈

M  N 

pmn fym (y)fzn (z)

y, z ∈ S1 ,

(3)

m=1 n=1

and the integral equation is tested by the following testing functions: tkl (y, z) (k = 1, 2, . . . , K; l = 1, 2, . . . , L)

y, z ∈ S1 .

(4)

For example, pulse approximating (fym (y), fzn (z)), and testing (tkl (y, z)) functions are used in [2], linear approximating and testing functions are applied in [3], while sinusoidal type global approximating and pulse testing functions are used in [4].

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I. Kiss et al. / Parallelization of Crack Signal Calculation Using CUDA

As a result, the discretized integral equation will be: N M  

 [jωμ0 ×

pmn

m=1 n=1

S1

 × lim

x→x±

⎤

g11 (x, y, z|x  = 0, y  , z  )fym (y  )fzn (z  ) dy  dz  ⎦ tkl (y, z) dydz =

S1

 =

i E1n (x = 0, y, z)tkl (y, z) dydz; S1

k = 1, 2, . . . , K, l = 1, 2, . . . , L.

(5)

Consequently the following linear equation system is to be solved: A p = b,

(6)

where

$ % • A (k−1)L+l,(m−1)N +n is the normal component of the electromagnetic field due to a surface current distribution described by fym (y)fzn (z) and tested by the testing functions tkl (y, z), • (b)(k−1)L+l is the incident field tested by the testing function tkl (y, z), $ % • p (m−1)N +n = pmn is the unknown coefficients of the surface current distribution.

One can see that the most time-consuming task, the calculation of the elements of A can be calculated independently from each other. This is the reason why the parallelization of the outlined solution can really decrease the calculation time needed to obtain the crack signal. Note also that the same conclusion can be derived if multiple cracks are considered as the solution of (1).

3. CUDA parallel programming model A CUDA program mainly consists of two parts. There is a so called host program, roughly speaking the function of which is to initialize the GPU for the computation while itself runs on the CPU only. The program running on the device (GPU) is usually called the kernel. As the kernel can operate only on data stored in the on-board memory of the device, all data must be transferred to the device prior to the computation. Similarly, the host program cannot directly access the on-board device memory, hence the result of the computations must be transferred back the computer’s main memory. These transfers are often act as the bottleneck of the whole computation. If the amount of data to be transferred is large, then due to the relatively slow PCI-E bus system, even with an excessively fast GPU the overall wall-time would increase, and the parallel execution would be pointless.

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121

3.1. Memory handling Since the available memory on todays average GPUs is limited in 1-2 GB, one may think that this memory constraint is just preventing any practical application, as time consume often arises from the need of manipulating large data sets. To overcome on this problem, one must not use of long standing algorithms: algorithms that do not need the whole data set to be stored in the memory all at once are ideally suited for this task. An other approach could be the decomposition of the original problem to smaller ones that fit into the memory constraint. The overall speed-up strongly depends on both data transfer and computation times. A commonly applied technique is to overlap data transfer with computation, which can be approached from CPU and/or GPU side. Namely, if a so-called asynchronous data transfer is applied, the control is immediately returned to the initializer of the transfer. Since latest graphic cards are capable to overlap kernel execution and memory transfers, partitioning the GPU memory to non-overlapping parts, the kernel may operate on one part, while the other(s) could be simultaneously loaded. As a result, one could keep both the CPU and the GPU busy, significantly decreasing the inertia of the data transfer. 3.2. Hardware design Output of the compiler regarding the GPU code is in a pseudo-assembly language (PTX), which is generally understandable by any CUDA capable GPU. Compilation of this code to the actual hardware instruction set is taking place at execution time by the device driver, therefore portability and backward-compatibility is also ensured. CUDA applies a Single Instruction Multiple Thread (SIMT) execution model, which is a variant on the Single Instruction Multiple Data (SIMD) architecture. At any given clock cycle, each streaming processor executes the same instruction, but operates on different data without the need of packing and unpacking the original data like in the case of SIMD (SSE2). Due to the SIMD architecture, thread divergence in a given core causes threads being in an inactive path to be executed, but not evaluated: all threads walk through all paths, significantly increasing the execution time. One may also note that thread divergence is only critical if occurs on numerous cores. A detailed overview on the topic can be found in [7]. 3.3. Design of parallelization The original program computing the ECT signal of multiple cracks (based on the formulations in Section 2.2) was written for a single core CPU. Most of the calculations are carried out analytically in the spatial frequency domain where the singularity of the kernel can be easily handled. Elements of matrix A in (6) are obtained in kn × km points of the spatial frequency domain followed by an analytical integration in the z direction. Spatial boundaries are determined adaptively, the kn ×km sampling points are distributed uniformly within the studied frequency domain. The main concept of the implementation can be found in [3] and [4], while this paper will focus on the design of parallelization. Generally, the first step during the design of parallelization is to obtain the execution times for the different parts of the program. In the given case, the assembly of the matrix elements is performed in subroutine 4, which requires about 45% of the total ex-

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I. Kiss et al. / Parallelization of Crack Signal Calculation Using CUDA

ecution time. The rest of the work is carried out in 3 other subroutines, where certain coefficients of the basis and testing functions related to different spatial positions are precalculated. These 3 subroutines requires about 15% of the total computation time each. Certain initialization process and post-processing is neglected for clarity. Fig. 2.a shows the schematic flowchart of the original program. After careful inspection of the program code, subroutine 4 is found the only part which can be efficiently parallelized, since each matrix element can be computed independently of the others. In the case of subroutine 1-3, numerous conditional statements are evaluated, resulting in divergent execution paths, which prevents the efficient execution on the SIMD architecture. Regretting this fact, these subroutines were also re-formulated for data parallel execution, but obtained wall-times confirmed theoretical considerations. 3.4. Concepts of parallelization Subroutine 4 will be parallelized and outsourced to the GPU while the rest of the program will be executed on the CPU. The execution path for the original single core CPU program is shown in Fig. 2.a: serial execution of subroutine 1-4 is carried out organized into a loop, in each cycle of which a spatial frequency component is computed. Note that the dots correspond to the neglected initialization procedure. 














    














 














  


 




  





Figure 2. Execution paths of the CPU and the two different CUDA models.

To replace subroutine 4, a CUDA kernel was carefully designed, performing the parallel computation over the different spatial frequency sampling points. Since the available memory on the GPU is less than that is required to store all the precomputed coefficients, the problem must be partitioned to smaller parts. Each partition contains a subset of the coefficients belonging to several spatial frequency points, the kernel will act on. Based on our investigations, the GPU performs the computation over the sampling points significantly less time (with about 2 magnitudes) than the computation of the coefficients takes on the host side. As a weird consequence, it become more important how the data is transferred to the GPU, as it is comparable to CPU computation time. Two CUDA programs were designed and implemented to investigate the effect of the different transfer methods. These differ only in the way how the coefficients are

123

I. Kiss et al. / Parallelization of Crack Signal Calculation Using CUDA

transferred to the GPU, while executing the same kernel. Both programs compute the required coefficients on the host side, enclosed in a loop containing subroutine 1-3. In Fig. 2.b, a semi-serial program model is shown. After a certain number of coefficients are computed in the host loop, a single asynchronous memory transfer occurs, followed by the invocation of the kernel. This enables the host loop (CPU) to keep computing during the time consuming transfers. The size of the subset to be transferred is equal to the total available memory on the GPU. The second program is shown in Fig. 2.c, and is based on the idea that memory transfer time can only be hidden if the CPU is busy with the computation of coefficients during the transfers. In order to achieve such a case, precomputed coefficients are transferred in smaller sets. The size of a subset to be transferred was determined to take insignificantly small time, hence its amount is limited in several MBs. In the given example, a data-set corresponding to km sampling points is chosen for such purpose. The kernel is invoked on the transferred data when the memory of the GPU is full up after numerous transfers.

4. Results

a)

transferred data

The CPU and the two CUDA programs were executed on a HP XW8600 workstation with a total of 32 GB memory, 2× Quad-Core Intel Xeon X5450 processors and an NVIDIA GTX 480 video card. 20 GB 10 GB 5 GB 2 GB 1 GB

7 MB 3 MB 1 MB

transfer in each cycle total amount of transfers

c)

speed-up [×]

b)

Sub_4 run time [s]

80

CUDA semi serial 60

CUDA overlapping CPU

40 20

6

0

5 4 3 2 1

200

400

600

800

1000

1200

1400

1600

1800

2000

km = kn = N Figure 3. a) amount of data for the “overlapping” transfer method (note that values on the y axis are shown in logarithmic scale); b) execution times of subroutine 4; c) measured relative speed up.

124

I. Kiss et al. / Parallelization of Crack Signal Calculation Using CUDA

Fig. 3.a shows the amount of data transferred in each cycle, as well as for the total problem in the “overlapping” case for different number of sampling points (note that the total amount of GPU memory is only 1.5 GB for the given hardware). Run-times with respect to subroutine 4 are shown in Fig. 3.b. Based on the amount of data transferred to the GPU (Fig. 3.a) and calculating with an average of 1 GB/s transfer rate, it can clearly be seen that a significant portion of time is spent on data transfer, rather than on (kernel) computation. The semi-serial CUDA computational model performed a bit worse than that of the CPU. The second CUDA model, applying overlapping data transfer and CPU computation, performed significantly better, preceding both the CPU and the semi-serial CUDA model. It must be emphasized that the kernel function itself is the same in both program models, only the applied data transfer technique varies. The results indicate that the execution time of the kernel of the implemented algorithm is negligible compared to data transfer time. The acceleration achieved by the overlapping CUDA model is shown in Fig. 3.c.

5. Conclusion In this paper the possibility of using CUDA for re-coding already existing single processor algorithms/programs was discussed. In the presented example by parallelizing only a fraction (subroutine 4 constitutes only about 10%) of the whole source code, a remarkable speed-up could be achieved. Drawbacks of the required memory transfers between host and device memory are shown together with some commonly applied techniques, that could be used to hide the inertia of the transfer. Application of overlapping memory transfers with CPU computations shown remarkable performance gain compared to the semi-serial data processing model. Although it would be possible to overlap the data transfers with kernel executions as well, in the present case due to the negligible time of kernel execution, similar results would be obtained. For problems having more intensive (time consuming) computations in the kernel, a trade-off in the amount of transferred data must be found to achieve optimal overall performance.

References [1] [2] [3]

[4] [5] [6] [7]

Online available: www.nvidia.com/cuda J.R. Bowler, Eddy current interaction with an ideal crack I. The forward problem, J. Appl. Phys., 75 (11) (1994), 8128 8137. J. Pavo, Reconstruction of Group of Cracks in Plate Specimens Using ECT Impedance Data, in Electromagnetic Nondestructive Evaluation (IV), S. S. Udpa, T. Takagi, J. Pavo and R. Albanese, Eds., IOS Press, Amsterdam, 2000, 204 211. J. Pavo, D. Lesselier, Calculation of eddy current probe signal with global approximation, IEEE Transaction on Magnetics, 42 (4) (2006), 1419 1422. A Garland, M.; Le Grand, S.; Nickolls, J.; Anderson, J.; Hardwick, J.; Morton, S.; Phillips, E.; Zhang, Yao & Volkov, V., Parallel Computing Experiences with CUDA, IEEE_M_MICR, 28 (2008), 13 27. Makino, J., & Taiji, M., Special Purpose Computers for Scientific Simulations The GRAPE systems (Chichester: John Wiley and Sons), 1998. T. Halfhill, Parallel Processing with CUDA, Microprocessor Journal, (2008).

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-125

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-134

Eddy Current Testing of Ferromagnetic Materials: Modelling of Flaws in a Planar Medium Chiara ZORNI a,1 , Christophe REBOUD a Marc LAMBERT b and Jean-Marc DECITRE a a CEA, LIST, Département Imagerie Simulation pour le Contrôle, F-91191 Gif-sur-Yvette, France b Département de Recherche en Électromagnétisme, Laboratoire des Signaux et Systèmes UMR 8506 (CNRS - SUPELEC - Univ Paris-Sud), 91192 Gif-sur-Yvette, France Abstract. Eddy Current Testing (ECT) is a standard technique in industry for the detection of surface breaking flaws in ferromagnetic materials such as steels. In this context, simulation tools can be used to improve the understanding of experimental signals, optimize the design of sensors or evaluate the performance of ECT procedures. CEA has developed for many years semi-analytical models embedded into the simulation platform CIVA [1] dedicated to non-destructive testing. Following a previous work carried out at the laboratory in the case of one flaw located in a cylindrical ferromagnetic part, the developments presented herein address the case of a flaw located inside a planar and ferromagnetic medium. The theoretical approach will be presented, as well as comparisons between simulation data obtained from the literature. Keywords. Integral formulation, Dyadic Green Functions, ferromagnetism, cracks, eddy current testing

Introduction Eddy current testing (ECT) is a standard technique in industry for the detection of surface breaking flaws in ferromagnetic materials such as steels. In this context, simulation tools can be used to improve the understanding of experimental signals, optimize the design of sensors or evaluate the performance of ECT procedures. CEA has developed for many years semi-analytical models embedded into the simulation platform CIVA [1] dedicated to non-destructive testing. Following a previous work [2] carried out at the laboratory in the case of one flaw located in a cylindrical ferromagnetic part, the developments presented herein address the case of one flaw located inside a planar [3] and ferromagnetic medium. Simulation results are obtained through the application of the Volume Integral Method (VIM) [4]. This approach has proved its efficiency when considering canonical geometries, mainly 1 Corresponding

Author E-mail: [email protected]

C. Zorni et al. / ECT of Ferromagnetic Materials: Modelling of Flaws in a Planar Medium

135

Figure 1. Configuration of the ECT problem.

due to the fact that, in those cases, analytical expressions of dyadic Green operators are available in the spectral domain. While only one integral equation, involving either the electric or the magnetic field, is needed to describe the non-magnetic case completely, in the ferromagnetic case two coupled integral equations have to be solved. Therefore, when considering the ECT of a single flaw, a system of two integrodifferential equations is derived from Maxwell equations. The numerical resolution of the system is carried out using the classical Galerkin variant of the Method of Moments [5]. Finally, the probe response is calculated by application of the Lorentz reciprocity theorem [6]. The resolution has been generalized to the ECT simulation of M flaws located in a planar stratified medium. The theoretical approach will be presented, as well as comparisons between simulation results and measured data obtained from the literature [7].

1. Theoretical formulation Let us consider the general configuration described in Figure 1: a planar, stratified and ferromagnetic medium consisting of N linear, isotropic and homogeneous layers. The first and the last layers are two air half-space of permeability ε0 and permittivity μ0 and a time harmonic source with implied time-dependence e−jωt is placed in the first layer (with ω = 2πf the angular frequency). The others k = 2, . . . , N − 1 layers are characterized by their conductivity σk , their permeability μk = μ0 μkr (μkr, being the k th layer relative permeability) and the complex permittivity ε˜k = ε0 + jσk ω −1 . One or more 3-D bounded  material(s) is contained in l = n, . . . , m layers and is characterized m by its volume Ω = l=n Ωl and its conductivity σld and permeability μdl . The approach consists in calculating the electric and magnetic fields, E and H respectively, in the volume of the defect Ω without considering the defect contribution. Then, the variations of the fields induced by the presence of the defect are computed in Ω. The volume integral formulation is derived by applying the Green’s theorem [4] to the Maxwell’s equations and involves the dyadic Green’s functions for a multilayered medium [3]. Let us introduce the fictitious electric and magnetic total (Eq. (1)) and incident (Eq. (2)) currents as: Jk (r) = Δσk (r) Ek (r) ,

Mk (r) = Δμk (r) Hk (r)

(1)

J0k (r) = Δσk (r) E0k (r) ,

M0k (r) = Δμk (r) H0k (r)

(2)

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C. Zorni et al. / ECT of Ferromagnetic Materials: Modelling of Flaws in a Planar Medium

where Δσk (r) = σk − σkd (r) and Δμk (r) = μk − μdk (r) are the electric contrast and the magnetic contrast functions respectively and Ek (r) and Hk (r) the total and E0k (r) and H0k (r) the incident electric and magnetic fields in the k th -layer. A system of two integro-differential equations gives the expression of the electric and magnetic fields in the k th -layer as: Jk (r) =

J0k (r)

− jωμk Δσk (r)

m   l=n

Ωl

   Gee kl (r, r ) · Jl (r ) dr

− jωΔμk (r)

m   l=n

Mk (r) =

M0k (r)

− Δσk (r)

m   l=n

Ωl 2

Ωl

   Gem kl (r, r ) · Ml (r ) dr

(3)

   Gme kl (r, r ) · Jl (r ) dr

− ω ε˜k Δμk (r)

m   l=n

Ωl

   Gmm kl (r, r ) · Ml (r ) dr ,

(4)

me mm em     where Gee kl (r, r ), Gkl (r, r ), Gkl (r, r ) and Gkl (r, r ) stand for the dyadic Green’s functions and correspond to the electric or magnetic field response at the point r of an unit point current source of electric or magnetic nature placed in r  and are solution of  the Helmholtz equation. Thanks to the duality principle, only the dyads Gee kl (r, r ) and me  Gkl (r, r ) have to be computed and the two others are respectively obtained through: me Gem kl (ε, μ) = Gkl (−μ, −ε)

(5)

ee Gmm kl (ε, μ) = Gkl (−μ, −ε)

(6)

Finally the response of the probe, in this case a single emitting/receiving coil, is given by: ΔZ = −

m  ' & 1  E0k (r  ) · Jk (r  ) + jωHk (r  ) · M0k (r  ) dr  2 I Ωk

(7)

k=n

where I is the feeding current of the probe. In order to numerically solve the system (Eq. (3)) and (Eq. (4)), a discretization by means of a Galerkin’s version of the method of moments [5] is applied. The volume of the flaw Ω is divided into NΩ parallelepiped voxels in which the electric and magnetic fields are taken as constant values. In doing so a linear system of equations is obtained where the system matrix is symmetric (from properties of symmetry of the Green dyads). This system, however, can be associated to stiff matrices since the electric and magnetic fields might differ by orders of magnitude depending on the characteristic impedance of the medium. From a numerical point of view, it is advantageous to equilibrate the linear system to solve in order to avoid numerical instabilities [8].

C. Zorni et al. / ECT of Ferromagnetic Materials: Modelling of Flaws in a Planar Medium

137

2. Numerical results for a single layer Our approach is validated in a single layer configuration at a frequency f = 1.5 kHz. According to our notation we have then N = 3 and k = 2, from now the latter will be implied. Its thickness e, its relative permeability μr , its conductivity σ and the corresponding skin depth δ are given in Table 1. e

μr

σ

δ

1.25 mm 100 1 MS m−1 2.3 mm Table 1. Geometrical and physical parameters of the ferromagnetic layer.

The ferromagnetic layer is affected by cuboid-shaped voids of length L, width w and depth d given in Table 2. Three kinds of defects are dealt with, the through-wall defect and two having a depth equal to 40 % of the thickness of the plate called “inner defect” when breaking the surface on the same side of the acquisition probe and “outer defect” when breaking the surface on the opposite side. L

w

d

6 mm 0.2 mm [40 %; [100 %] e Table 2. Description of the defect affecting the layer.

The variation of impedance ΔZ is simulated by moving a single emitting/receiving coil along the largest dimension of a defect Ω affecting the ferromagnetic layer. The acquisition configuration is described in Table 3. outer diameter 3.2 mm

inner diameter

height

number of turns

lift-off

1.2 mm 0.8 mm 140 0.5 mm Table 3. Description of the acquisition configuration.

feeding current 1 mA

2.1. Comparison with data from literature A first comparison between our semi-analytical model and data from the literature [7] is presented for the configuration described in the previous section. A ferromagnetic plate with an “outer defect” of 40 % of the plate’s thickness is considered. The number of voxels NΩ used to discretize the volume of the defect is 20 × 20 × 6 on x, y and z axis respectively. The result of this simulation is compared with a finite-elements model result from literature [7]. In Figure 2 the impedance variations obtained with the two different models are superposed and a good agreement between the models is observed. 2.2. Comparison with the equivalent ECT configuration in cylindrical geometry An equivalent configuration in cylindrical geometry has been simulated (see Figure 3) in order to test the behavior of our model in different ECT cases. The model in cylindrical geometry is integrated in CIVA and has already been experimentally validated [2]. In order to be able to simulate a configuration as close as possible to the previous one

138

C. Zorni et al. / ECT of Ferromagnetic Materials: Modelling of Flaws in a Planar Medium 0

x 10

6

−1

Imaginary part [ohm]

−2 −3 −4 −5 −6 −7 −8

iterature model

−9

−6

−5

(a)

−4 −3 Real part [ohm]

−2

−1

0 x 10

6

(b)

Figure 2. Simulated ECT configuration (a) and the corresponding results (b) for a 40 % depth outer flaw. Signals show the impedance variations corresponding to the passage of the emitting/receiving coil over the flaw. The result is compared with a finite element result from the literature [7]

(a)

(b)

Figure 3. Equivalent ECT configuration in cylindrical geometry (a) and the corresponding angular extension ϕ (b). Geometrical and physicals parameters are given in Table 4.

outer diameter

inner diameter

ϕ

w

d

42.5 mm

40 mm

17.19◦

0.2 mm

[40 %; 100 %] e

(a) Tube parameters (b) Defect parameters affecting the tube Table 4. Parameters of the equivalent ECT configuration in cylindrical geometry described in Figure 3.

the inner and outer diameters of the tube (given in Table 4a) have been chosen large enough with respect to those of the acquisition probe. The geometrical parameters of the corresponding 100 % defect and 40 % inner and outer defects are reported in Table 4b. To validate the similarity between the planar and the cylindrical configurations both simulated results are compared in the case of an outer defect (see Figure 4). As expected the two ΔZ have the same shape and the same order of magnitude. Two others configurations have been then simulated in planar and cylindrical geometries: an inner defect of 40 % (Figure 5) and a through-wall crack (Figure 6). Those results show a good agreement between the two ferromagnetic models even if, for the 100 %-crack, a discrepancy between the two curves exists and might be caused by the two different geometries.

C. Zorni et al. / ECT of Ferromagnetic Materials: Modelling of Flaws in a Planar Medium

139

−6

x 10 −1

Imaginary part [ohm]

−2 −3 −4 −5 −6 −7 −8

cylindrical model planar model −8

−6

−4

Real part [ohm]

(a) Comparison between the planar configuration and the cylindrical one.

−2

0 −6

x 10

(b)

Figure 4. Results for a 40 % depth outer flaw. Signals show the impedance variations corresponding to the passage of the emitting/receiving coil over the flaw. Comparison with the equivalent case in cylindrical geometry of CIVA.

−5

x 10 −2

Imaginary part [ohm]

−4 −6 −8 −10 −12 −14 −16

cylindrical model planar model −10

(a)

−5

Real part [ohm]

0

5 −5

x 10

(b)

Figure 5. Results for a 40 % depth inner flaw. Signals show the impedance variations corresponding to the passage of the emitting/receiving coil over the flaw. Comparison with the equivalent case in cylindrical geometry of CIVA.

3. Conclusions and perspectives A model has been developed in order to simulate the response of the ECT probe, consisting in a set of emitting and receiving coils, to the presence of a flaw in a planar stratified and ferromagnetic medium. Simulations results and comparisons with the literature and

140

C. Zorni et al. / ECT of Ferromagnetic Materials: Modelling of Flaws in a Planar Medium

0

x 10

5

Imaginary part [ohm]

−2

−4

−6

−8

−10 cylindrical model planar model

−12 −14

(a)

−12

−10

−8 −6 Real part [ohm]

−4

−2

0 x 10

5

(b)

Figure 6. Results for a 100 % depth flaw. Signals show the impedance variations corresponding to the passage of the emitting/receiving coil over the flaw. The result is compared with a finite element result from the literature. Comparison with the equivalent case in cylindrical geometry of CIVA.

the equivalent cylindrical model of CIVA carried out in the case of a single layer and a single emitting/receiving coil show a good agreement between the simulated signals. Experimental validations are currently in progress and will take into account also the stratified case and the multiple flaws aspect. The perspective for this work is the extension of the model to simulate the response of a magnetic probe containing GMR elements.

References [1] [2]

[3]

[4] [5] [6] [7] [8]

CIVA: State of the art simulation platform for NDE. http://www-civa.cea.fr. A. Skarlatos, G. Pichenot, D. Lesselier, M. Lambert, and B. Duchêne. Electromagnetic modeling of a damaged ferromagnetic metal tube via a volume integral formulation. IEEE Trans. Mag., 44:623–632, 2008. Séverine Paillard, Grégoire Pichenot, Marc Lambert, and Hubert Voillaume. Eddy current modelling for inspection of riveted structures in aeronautics. In S. Takahashi and H. Kikuchi, editors, Electromagnetic Non–Destructive Evaluation (X), Studies in Applied Electromagnetics and Mechanics, pages 25–32. IOS Press, Amsterdam, 2007. Weng Cho Chew. Waves and Fields in Inhomogeneous Media. Wiley-IEEE Press, New-York, 1999. R.F. Harrington. The method of moments in electromagnetics. J. Electromagn. Waves Appl., 1:181– 200(20), 1987. B. Auld, F. Muennemann, and M. Riaziat. Research Techniques in Nondestructive Testing, volume 7, chapter Quantitative modelling of flaw responses in eddy current testing, pages 37–76. 1984. Haoyu Huang, Toshiyuki Takagi, and Tetsuya Uchimoto. Fast numerical calculation for crack modeling in eddy current testing of ferromagnetic materials. J. Appl. Phys., 94(9):5866–5872, 2003. A. Abubakar and P. M. van den Berg. Iterative forward and inverse algorithms based on domain integral equations for three-dimensional electric and magnetic objects. J. Comp. Phys., 23:236–262, 2004.

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-141

141

Efficient Propagation of Uncertainty in Simulations Via the Probabilistic Collocation Method Jeremy S. KNOPPa,1, John C. ALDRINb, and Mark P. BLODGETTa a

Air Force Research Laboratory, USA b Computational Tools, USA

Abstract. Eddy current models have matured to such a degree that it is now possible to simulate realistic nondestructive inspection (NDI) scenarios. Models have been used in the design and analysis of NDI systems and to a limited extent, model based inverse methods for Nondestructive Evaluation (NDE). The science base is also being established to quantify the reliability of systems via Model Assisted Probability of Detection (MAPOD). In realistic situations, it is more accurate to treat the input model variables as random variables rather than deterministic quantities. Typically a Monte Carlo simulation is conducted to predict the output of a model when the inputs are random variables. This is a reasonable approach as long as computational time is not too long; however, in most applications, introducing a flaw into the model results in extensive computational time ranging from hours to days, prohibiting Monte Carlo simulations. Even methods such as Latin Hypercube sampling do not reduce the number of simulations enough for reasonable use. This paper presents the Probabilistic Collocation Method as a non intrusive alternative to other uncertainty propagation techniques. Keywords: eddy current, Polynomial Chaos, Probabilistic Collocation Method

Introduction Recent model development efforts have demonstrated significant advances in the simulation of eddy current inspection scenarios [1-3]. This work is a critical component of a strategy to use modeling and simulation in NDE to reduce the cost and experimental burden of Probability of Detection (POD) studies, characterize damage, and optimize probe design and inspection configuration. The authors have investigated the utility of several numerical methods for electromagnetic NDE. These methods include analytical methods, the finite difference method, the finite element method (FEM), meshless FEM, the boundary element method (BEM), and the volume integral method. In addition to these methods, hybrid methods are also being developed [2]. While incremental advances in computational efficiency are expected, the future development of model-assisted probability of 1 Air Force Research Laboratory (AFRL RXLP), Wright Patterson AFB, OH [email protected]

45433, USA,

Email:

142

J.S. Knopp et al. / Efficient Propagation of Uncertainty in Simulations via the PCM

detection (MAPOD) protocols and model-based inversion schemes should not depend on a revolution in computational efficiency. One technical capability necessary for the realization of MAPOD and deployable model-based inverse methods is the propagation of uncertainty in input variables. In this work, variable refers to a measurable quantity, and parameter refers to a quantity that must be estimated such as liftoff. Stochastic numerical methods have been developed to propagate uncertainty efficiently without relying solely on advances in computational power. Significant advances in stochastic computation have been made especially in the last 20 years. This paper briefly traces the development of stochastic numerical methods pertinent to NDE modeling and simulation. The probabilistic collocation method (PCM) is introduced and applied to two eddy current forward models.

1. Probabilistic Collocation Method Spectral representation of uncertainty involves decomposing a random variable into deterministic and stochastic components. Following the work of Norbert Wiener on Homogeneous Chaos [4], Cameron and Martin pointed out that any second-order functional of Brownian motion can be expressed as a mean-square convergent series in terms of infinite-dimensional Hermite polynomials in Gaussian variables [5]. Any random process with finite second-order moments, (which encompasses most physical phenomena) can be represented by a Polynomial Chaos expansion using Hermite polynomials and will converge according to the Cameron-Martin theorem. If this random process is Gaussian, the convergence is exponential. An important property of Hermite polynomials is that they are orthogonal with respect to Gaussian probability measure. In fact for Gaussian processes, optimal convergence is achieved with the use of Hermite polynomials because the weighting function is the same as the probability density function (PDF) for the Gaussian distribution. To illustrate, the definition of an orthogonal polynomial with respect to a given weighting function w(x) is given by: b

( f ⋅ g )w = ∫ f ( x) g ( x) w( x)dx = 0

(1)

a

The inner product of functions f(x) and g(x) is zero if they are orthogonal with w(x). The only polynomial functions that satisfy this for the case where the weighting function is equal to the PDF of a standard normal distribution are Hermite polynomials. Ghanem and Spanos combined this concept with the finite element method to simulate problems in solid mechanics [6]. For non-Gaussian processes, the convergence is not optimal, but fortunately there are other orthogonal polynomial sets for other general types of random variables that converge exponentially [7]. In work mentioned thus far, the formulations are often intrusive, meaning that alternation of deterministic code is necessary for implementation. A non-intrusive method was introduced in the mid-1990’s [8]. Essentially, a reduced order polynomial form of the model is derived with minimal simulations. The input values for these simulations are derived from the roots of orthogonal polynomials which are dependent only on the input distributions. Hermite polynomials are associated with Gaussian distributions as described in the preceding paragraph. The weighting function for the

J.S. Knopp et al. / Efficient Propagation of Uncertainty in Simulations via the PCM

143

Uniform distribution is simply a constant on an interval bounded by [a,b]. Legendre polynomials are orthogonal with this weighting function.

2. Case Study 1. Application of the Probabilistic Collocation Method is model independent, but the decision of what order and whether to include interaction terms does depend on the complexity of the mapping of input variables to the output response. The orthogonal polynomials and their associated roots are dependent on the type of input distribution and its parameters. For this case study, the team15B workshop problem presented by Steve Burke is used [9]. All simulations are conducted using VIC-3D®. The only variable that is changed in this example is the frequency, which is 500 Hz here instead of 7 kHz. In this problem, the probe is scanned along the notch and the real and imaginary components of the impedance are measured. A peak in the magnitude of the impedance is observed when the center of the coil translated along the notch at a distance of -12 mm and 12 mm away from the origin which is the center of the notch. The objective of this exercise is to predict the probability density function (PDF) of the peaks of the real and imaginary components of the impedance when the liftoff of the coil is uniformly distributed between 1.53 mm and 2.53 mm, and the depth of the notch is normally distributed with a mean of 5 mm and standard deviation of 1 mm. In the original problem the coil liftoff is 2.03 mm and the depth of the flaw is 5 mm. The first step is to derive orthogonal polynomials with respect to the input distributions. From now on the parameter liftoff will be denoted by ‘A’, and notch depth will be denoted by ‘B’. For liftoff, Legendre polynomials associated with that particular distribution and parameter set are shown in equation 2. For the depth, the Hermite polynomials are shown in equation 3.

L1 ( A) = A − 2.03 L2 ( A) = A2 − 4.06 A + 4.0376 L3 ( A) = A3 − 6.09 A2 + 12.2127 A − 8.0609 4

3

(2)

2

L4 ( A) = A − 8.12 A + 24.5111A − 32.5917 A + 16.1041 L5 ( A) = A5 − 10.15 A4 + 40.9312 A3 − 81.9626 A2 + 81.4899 A − 32.1796 H 1 (ζ ) = ζ H 2 (ζ ) = ζ 2 − 1 H 3 (ζ ) = ζ 3 − 3ζ

H 4 (ζ ) = ζ 4 − 6ζ 2 + 3 H 5 (ζ ) = ζ 5 − 10ζ 3 + 15ζ

(3)

Note that since the mean of the Gaussian distribution is 5, parameter B is translated by 5.

B = 5 + H1 (ζ )

(4)

Next, a first order model might be used to approximate the real model. In this case, there are three unknowns X0, X1, and X2 as shown in equation 5. Since we are interested in both the resistance and reactance, this process is done separately for each.

144

J.S. Knopp et al. / Efficient Propagation of Uncertainty in Simulations via the PCM

(a)

(b)

Figure 1. Change in the (a) real and (b) imaginary part of the impedance due to the plate and flaw. Three simulations are required to solve for the three coefficients. Four pairs of collocation points for the inputs of the simulations are available from the roots of the 2nd order polynomials. Three pairs are selected to solve for the three unknowns. L 1 and H1 are simply evaluated at the three pairs of collocation points. This is all that is needed for the a 1st order approximate model. Then a Monte-Carlo simulation can be conducted on this simple model to calculate the PDF of the resistance and reactance. To check the accuracy of this approximation, the next higher order collocation points are necessary. The roots of the 3rd order orthogonal polynomials are used and six simulations using the full model are conducted and compared with the approximate model. Ultimately nine simulations are necessary for construction and evaluation of the 1st order approximate model. Fortunately the same six simulations used for the error check of the 1st order model can be used to construct the 2nd order approximate model. The 4th order orthogonal polynomials are then used to check the accuracy of the 2nd order approximate model requiring eight more simulations for a total of fourteen simulations. The authors have generally found that a 3rd order approximate model with one interaction term is usually sufficient to predict output PDF’s with good accuracy for forward eddy current simulations, but there may be situations where higher order approximations with more interaction terms are needed.

Yˆ = X 0 + X 1 L1 ( A) + X 2 H1 ( B)

(5)

The form of the 3rd order reduced model as described in equation 6 has eight coefficients, one of which is an interaction term. Yˆ = X

0

+ X 1 L1 ( A ) + X 2 H 1 (ξ ) + X 3 L 2 ( A ) + X 4 H 2 (ξ )

+ X 5 L 3 ( A ) + X 6 H 3 (ξ ) + X 7 L1 ( A ) H 1 (ξ )

(6)

To solve for the eight unknowns, eight simulations must be run. The roots of the 4th order Legendre and Hermite polynomials are used to select the input values for A and B in these simulations. This is done separately for the real and imaginary components of the impedance. Once again, everything is known except for the X coefficients. The resulting system of equations is then solved and the coefficients are

J.S. Knopp et al. / Efficient Propagation of Uncertainty in Simulations via the PCM

145

listed in Table 1 for both the real and imaginary components of the impedance. Incidentally, X0 is the expected value, which is one of the primary benefits of using orthogonal polynomials. As expected, the interaction term X7 is close to zero in both cases. To check the error of this third order approximation, the roots of the 5 th order polynomials are used to select collocation points. Ten more simulations are needed for comparison with the reduced order model predictions. The results of the simulations and the results of the reduced model are displayed in Table 2. Table 1. Coefficients for 3rd order approximation model. Model term X0 X1 X2 X3 X4 X5 X6 X7

Real 0.9693 0.2209 0.0012 0.0284 0.0004 0.0050 0.0001 0.0003

Imaginary 2.4132 0.4386 0.0072 0.0479 0.0011 0.0077 0.0003 0.0018

Table 2. Evaluations of original and approximation model for error calculation. Y real 1.027 1.0284 1.0306 0.9656 0.9670 0.9690 0.9084 0.9098 0.9117 0.8774

Yˆ real 1.0270 1.0280 1.0305 0.9656 0.9666 0.9690 0.9084 0.9092 0.9116 0.8778

Y imaginary

Yˆ imaginary

2.5444 2.5272 2.5202 2.4219 2.4059 2.3994 2.3066 2.2918 2.2857 2.2073

2.5415 2.5295 2.5214 2.4195 2.4081 2.4007 2.3043 2.2937 2.2869 2.2053

The residual is defined as the difference between the full and reduced model in equation 7, and the sum of squares of the residuals is defined in equation 8. The relative sum of squares of the residuals is used to quantify the error in the approximation. The relative sum of squares of the residuals is calculated by simply dividing by the expected values as shown in equation 9. These quantities are summed over the model results for each collocation point.

ε

Y

ssr =

rssr =

Yˆ

∑ε i

n ssr E[Yˆ ]

(7) 2 i

(8)

(9)

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The errors for the real and imaginary parts are given by: ssr(resistance) = and 2.9428×10-4, rssr(resistance) = 3.0359×10-4, ssr(reactance) = 0.0020, rssr(reactance) = 8.4790×10-4. Now there are two 3rd order polynomials with good accuracy for the real and imaginary components of the impedance. Monte Carlo simulations can now be run with ease on this 3rd order approximate model. The PDF for the real and imaginary component of the impedance is shown in Figure 2(a) and 2(b) respectively. 6

25

5

2

4

P DF

PDF

15 3

1 2 05

1

0 0 85

09

0 95 1 Resistance

1 05

11

(a)

0 27

26

25

24 23 Reactance

22

21

2

(b)

Figure 2. PDF of the (a) real and (b) imaginary component of the impedance.

3. Case Study 2. A second case study is presented for the characterization of a gap between multiple plates, representing the problem of characterizing corrosion at the faying surface of a multilayer aircraft structure. A diagram of the problem is shown in Figure 3 including material properties and dimensions. In this hypothetical study, the thickness and conductivity of the layer are treated as random variables. The conductivity of the top plate is assumed to be a normal random variable with a mean value of 1.876×107 S/m and standard deviation of 3.384×106 S/m as shown in Figure 4(a). The liftoff is defined as a uniform random variable with the range of 0.55 +/- 0.05 mm as shown in Figure 2(b). VIC-3D® was used to generate the simulated results for the study. The gap between the plates was fixed at 0.3 mm and the frequency for the study was set to 4.0 kHz. Both 1st order and 2nd order PCM models were evaluated for this case requiring only 3 and 6 model calls respectively. Monte Carlo simulations were also run with 100,000 model calls used in the study.  Ϭ͘ϴϭŵŵ ϲ͘ϱϱŵŵ

Ěnj ĚŚ

Figure 3. Diagram of case study 2 problem.

ϳ

σ1сϭ͘ϴϳϲϭϬ ^ͬŵ ϳ σairсϬ͘ϬϭϬ ^ͬŵ ϳ σ2сϭ͘ϴϱϲϭϬ ^ͬŵ

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J.S. Knopp et al. / Efficient Propagation of Uncertainty in Simulations via the PCM 600

200

160

500

140

150

120

400

100 300

100

80 60

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40 100

MC PCM

20

0 15

2

25

σ (S/m)

7

x 10

(a)

0 52

0 54

0 56

0 58

06

(b)

dz (mm)

0 0 085

0 09

0 095

R g

250 200 X

150 100 50

MC PCM 0 71

0 72

X

0 73

0 704

0 704

0 706

0 706

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0 712

X

300

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0 05

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(d)

(c)

0 72 0 09

0 091 R

0 092

0 093

(e)

0 09

0 091 R

0 092

0 093

(f)

Figure 4. (a) Conductivity and (b) liftoff input distributions with ouput (c) resistance and (d) reactance output 1D distributions and (e) joint distribution calculated using PCM. (f) A joint distribution calculated using Monte Carlo simulations is provided for comparison. Results for the 2nd order PCM model are presented in Figures 4(c)-(f). The results in Figures 4(c)-(d) show that the resistance is basically distributed uniformly and the reactance is basically distributed as a normal random variable. This relationship is expected based on the different effect of liftoff and conductivity changes in the impedance plane. A comparison of the joint distribution calculated using both PCM and Monte Carlo methods are shown in Figures 2(e) and 2(f) respectively. By observation, good agreement was achieved using PCM with Monte Carlo methods while only requiring 6 model calls here. Values for the error between the PCM and Monte Carlo simulations for the 1st order PCM model, ssr and rssr, were 43.58 and 0.3177 respectively. Error values for the 2nd order PCM model, ssr and rssr, were 15.49 and 0.1129 respectively. Thus, the 2nd order model provides a 64.5% reduction in the error between the PCM and Monte Carlo simulations with respect to the 1 st order model. In conclusion, the PCM approach is highly efficient at propagating parameter variation through models with minimal model calls.

4. Summary A non-intrusive approach to propagating random inputs in eddy current forward models was presented. The selection of collocation points in this method depends on the type and parameters of the input statistical distribution and not the model itself. Prediction of the PDF can be achieved with fewer simulations than traditional uncertainty propagation methods. Future work will investigate using the method with

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more input variables and also for inverse problems. The robustness of this method for inverse problems will likely be much more sensitive to choice of order and interaction terms.

5. Acknowledgements Funding was provided in part, by the Air Force Office of Scientific Research. Many thanks to Matt Cherry for reviewing the manuscript.

References [1] [2]

[3]

[4] [5] [6] [7] [8] [9]

J. S. Knopp, J. C. Aldrin, and K. V. Jata, Computational Methods in Eddy Current Crack Detection at Fastener Sites in Multi Layer Structures, Nondestructive Testing and Evaluation, 24 (2009), 103 120. A. Skarlatos, C.G. Pascaud, G. Pichenot, G. Cattiaux and T. Sollier, Modelling of steam generator tubes inspection in the proximity of support plates area via a coupled finite elements volume integral method approach, in Electromagnetic Non Destructive Evaluation (XII), Studies in Applied Electromagnetics and Mechanics, Y. K. Shin, H. B. Lee, and S. J. Song, (Eds.). Amsterdam, IOS Press (2009), 51 58. H. A. Sabbagh, J. C. Aldrin, R. K. Murphy, and E. H. Sabbagh, Application of Model Based Inversion to Eddy Current NDE of Heat Exchanger Tubing, in Electromagnetic Non Destructive Evaluation (XII), Studies in Applied Electromagnetics and Mechanics, Y. K. Shin, H. B. Lee, and S. J. Song, (Eds.). Amsterdam, IOS Press (2009), 26 33. N. Wiener, The homogeneous chaos. American Journal of Mathematics, 60 (1938), 897 936. R. H. Cameron and W. T. Martin, The orthogonal development of non linear functionals in series of Fourier Hermite functionals. Annals of Mathematics, 48 (1947), 385 392. R. G. Ghanem and P. D. Spanos, Stochastic finite elements: a spectral approach. Springer Verlag, New York, 1991. D. Xiu and G. E. Karniadakis, The Wiener Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24 (2002), 619 644. M.A. Tatang, W.W. Pan, R.G. Prinn, and G.J. McRae, An efficient method for parametric uncertainty analysis of numerical geophysical model, J. Geophy. Res., 102 (1997), 21925 21932. www.compumag.org/jsite/images/stories/TEAM/problem15.pdf

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Computation of the magnetic field due to a defect embedded in a planar stratified media: Application to AC field measurement techniques Denis PRÉMEL 1 and Grégoire PICHENOT CEA, LIST, Centre de Saclay, F-91191 Gif-sur-Yvette cedex, France Abstract. Eddy current techniques are useful for the detection and the characterization of flaws in conductive structures. The flaw signal results from the measurement of the local punctual value of the perturbed magnetic field above the metal surface in the vicinity of the defect by using some magnetic field sensor (Giant Magneto Resistance sensor (GMR) or Giant Magnetic Impedance sensor (GMI). This paper aims to describe a semi-analytical numerical model integrated into the CIVA platform which is able to compute the flaw signal due to a given notch embedded in a planar stratified media. The inducer may be chosen in a list of available exciting coils into CIVA. Some numerical experiments and a comparison between simulated data and experimental data show the validity of the new developments. Keywords. Eddy current non destructive testing, Green’s dyad formalism, Giant Magneto-Resistance sensor, Giant Magneto-Impedance sensor

1. Introduction Eddy current techniques are very useful for the detection and the characterization of flaws in conductive structures. Eddy currents are induced in the workpiece under test by carrying a sinusoidal current in one or a set of exciting coils. According to the operating frequency, eddy currents induced in a thin "skin" near the surface of the conductive media interact with a flaw in such a way that currents flow around the ends of the defect and down the faces of the defect. The deviation of eddy currents results in the perturbation of the magnetic field above the metal surface and in the vicinity of the defect. The flawed signal is analyzed in order to locate and size surface defects. Considering Non Destructive Techniques (NDT), the variations of the magnetic field can be detected by the changes in the impedance of the exciting coil as it is commonly achieved in Eddy Current (EC) methods. The flaw signal is thus due to the global variation of the perturbed magnetic field. An alternative NDT method, Alternating Current Field Measurement (ACFM) consists in analyzing the flaw signal provided by some magnetic field sensor as Giant Magneto-Resistance (GMR) or Giant Magneto Impedance sensors [1,2,3,4]. 1 Corresponding

Author: Denis Prémel, CEA LIST; E-mail: [email protected]

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The flaw signal results from the measurement of local, punctual values of the surface magnetic field. This signal is obtained by using a tiny inductive sensor or a magnetic field sensor [5]. ACFM technique is very useful for sizing any crack with a simple geometry. The prediction of crack parameters (i.e. the length, the opening and the depth) from the magnetic field is of great interest in practice. The resolution of this inverse problem requires preliminarily solving efficiently the forward problem, i.e. to be available to compute the components of the magnetic field resulting from the interaction of the crack with eddy currents generated by some appropriated inducer. This paper aims to describe a numerical model based on the volume integral approach [6,7,8] which allows one to compute the flaw signal due to a given notch embedded in a planar stratified media. The inducer may be chosen arbitrarily from a list of exciting coils [9,10] available into CIVA [11] (a NDT numerical platform dedicated to several NDT techniques). In ACFM techniques, rectangular coils or current foils are preferably used in order to generate a uniform current flow orientated perpendicularly to the length of the flaw. This numerical model is firstly numerically validated by using two kinds of numerical models. These ones differ from the observation equation which is used for computing the response of the magnetic sensor. Then, some validation experimental results are presented. These new developments, translated into new functionalities in the last version of CIVA allow one to conduct some parametric studies such as the lift-off of the magnetic sensor, the tilt of the inducer, and other parameters which could be able to influence the sizing of the defect by using one or two components of the magnetic field. This work precedes also some work dedicated to the inversion problem [12].

2. An example of ECT configuration Figure 1 displays an example of ECT configuration consisting of a stratified slab affected by flaws. Eddy currents in the slab are induced by an exciting coil driven by an alternative current of angular frequency ω. Into the CIVA software, this coil may be chosen among cylindrical coils, with a ferrite core or not, or rectangular coils. In this figure, we consider two rectangular coils in order to approach the behavior of a uniform current in the Y direction. In this figure, we also assume a magnetic sensor which is able to provide the three components of the perturbed magnetic field due to the presence of the defects. It is important to note that the response of the sensor is obtained taking into account the sensitivity of the sensor, expressed in Volts per Tesla and that the response results from the difference between the field obtained in the presence of the flaw and the field obtained when there is no flaw. The computation module may consider an arbitrary number N of layers made of materials being linear, isotropic and not magnetic (with the permeability of the vacuum denoted by μ0 ). The conductivity σl of each layer is constant, except when there is a flaw. This one is indeed represented by local variations of the conductivity σ(r) in the lth layer. The continuation of this paper is organized as follows. In section 3, the eddy current modeling problem is solved by using the Volume Integral Method implying a system of two integral equations for which the kernels are based on the Green’s dyad formalism. In the previous version of the CIVA platform, the computation of the e.m.f induced in a receiving pick-up coil is available but we aim at the addition of new functionalities in

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151

Figure 1. An example of ECT configuration.

order to have the capability to compute the punctual values of each component of the perturbed magnetic field above the flawed material. So, two approaches are considered for obtaining the numerical solutions of the forward problem. These two approaches are used for the numerical validation of the new functionalities. Numerical results used for the numerical validation are compared in section 4 while a real experiment is proposed in section 5. Finally experimental data are compared with simulated data in order to show the experimental validation. A short conclusion follows in section 6.

3. The Volume Integral Method and the specific dyad for the problem The computation of the perturbed magnetic field above the plate requires computing firstly the electrical internal field in a finite domain surrounding the flaw. Each layer may include one finite volume containing an object and the total internal field in each layer k results from the interaction from the primary field Epk (r) in the layer due to the driving probe and the perturbation field due to a set of elementary flaws, each one being considered in a single layer l. The total electric field in each layer, denoted by Ek (r), is given by: Ek (r) =

Epk (r)

− jωμ0

N   l=1

Gkl (r, r ) [σl − σ(r )] El (r ) dτ (ee)

flaw

(1)

The contribution is null if there is no flaw in the lth layer (σ(r ) = σl ). The superscript (ee) means that we compute the components of the electrical field due to an unit point source which is a solution of: ∇ × ∇ × Gkl (r, r ) − kk2 Gkl (r, r ) = δkl I δ(r − r ). (ee)

(ee)

(2)

In this last equation, the observation point r is assumed to be in the layer k while the source point r is in the layer l. δkl stands for the Kronecker symbol and I is the unit dyad. According to the quasi-static regime, the wave number kk2 in the k th layer is given

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by kk2 = jωμ0 σk . The Green’s dyads satisfy as usually the appropriated boundary conditions at the infinity in the transverse directions and at the interfaces between two different layers in the normal direction to the planar surface of the stratified medium. The analytical expression of the Green’s dyad corresponding to a multilayered planar medium is given in [13]. The total internal field in each layer appears inside and outside the integral. This state integral equation must be solved numerically by the Moment Method (MoM) [14]. Knowing the total electrical field in each layer, the perturbed magnetic field can be computed above the plate, in the air region 1, by an observation equation which introduces (me)

the Green’s dyad G1k (r, r ). The superscript (me) means that the components of the magnetic field is calculated due to a current dipole: (me)

Gkl

(r, r ) = ∇ × Gkl (r, r ) (ee)

(3)

The total perturbed magnetic field takes into account all the contributions of each layer k:

B1 (r) = −μ0

N   k=1

flaw

G1k (r, r ) [σk − σ(r )] Ek (r ) dτ (me)

(4)

This equation has been implemented into CIVA. In order to validate these new developments, some other numerical data have been computed by using another numerical code which has been previously validated. Let us consider that the components of the magnetic field can be estimated by the e.m.f induced in a tiny pick-up coil when the section of the pick-up coil tends towards zero. In this case, the response of three receiving pick-up tiny coils is given by the changes in the mutual impedance and can be obtained via the reciprocity theorem: I1 I2 ΔZ = −

N   l=1

flaw

[σl − σ(r)] El (r) · Epl (r) dτ

(5)

where Epl (r ) stands for the primary field that would be induced by the receiving coil in the flawed region, in the lth layer, if it was driven by a current I2 , and I1 is the driving current of the exciting coil. The total electrical field El (r) in the lth layer comes from the numerical resolution of equation (1). According to the orientation of the pickup receiving coil, one can obtain an approximation of one component of the magnetic field by using the Faraday-Lorentz law. The numerical results which can be obtained by these two approaches can be now compared in order to show the validity of these new functionalities.

4. Numerical Validation Figure 2 displays the overview and the front view of an ECT configuration consisting of a non magnetic slab constituted by four layers. The thickness of each layer is fixed at

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153

0.8 mm, the values of the conductivities of each layer expressed in MS/m are given by σ1 = 0.1, σ2 = 0.5, σ3 = 1, σ4 = 10. The operating frequency is chosen at 100 kHz and let us consider two notches. The first one is breaking the surface of the first layer, it is 2 mm length, 0.3 mm depth and its opening is 0.1 mm. The second flaw is embedded at the top of the third layer, its length is equal to 4 mm, its depth is 0.5 mm and its opening is also 0.1 mm. These two flaws are differently orientated, the first one is orientated along the X axis while the second one is orientated along the Y direction. The eddy current (EC) probe is constituted by two exciting rectangular coils. For each one, the inner width is 4 mm , the inner length is 8 mm and the height is equal to 0.1 mm. The number of turns is 5 and finally the width of the current foil is 1 mm.

Figure 2. An overview (on the left) and a front view (on the right) of an ECT configuration used for a numerical validation.

The EC probe is scanning along three lines in the X direction and three values of the Y position have been chosen in order to verify the validity of the results in the two directions of scanning. Figure 3 and 4 show a comparison between the two numerical approaches resulting from the implementation of equations (4) and (5). The real and the imaginary parts of the Bx , Bz components are respectively shown. Three curves are displayed corresponding to three values of the Y position of the probe. These numerical results show a good agreement between the two numerical approaches. In the next section, an experimental validation is achieved. 5. Experimental validation Experimental data have been obtained from an experimental set-up which is depicted in Figure 5. Let us consider a non magnetic slab made of Inconel 600, the conductivity is assumed to be 1.02 MS/m. The operating frequency is 100 kHz. Eddy current are induced in the slab by a rectangular coil which is etched on a flexible film. The inner width of the coil is 23 mm, the inner length is 62 mm and the height is equal to 35 μm. The number of turns is 100 and finally the width of the current foil is 7 mm. The distance from the bottom of the exciting coil to the slab is about 2 mm. A Giant Magneto Resistance sensor (GMR) measures the Bx component of the magnetic field. The EC experimental signal is obtained by subtracting the response of the probe in the flawed region and the

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Figure 3. Real and Imaginary parts on the Bz component.

Figure 4. Real and Imaginary parts on the Bx component.

signal without the flaw. The distance from the GMR to the target is about 0.1 mm but this value can be affected by an uncertainty due to the encapsulation of the sensitive part of the sensor in the chip. The thickness of the slab is 1.55 mm and we consider a first notch for a preliminary procedure denoted by "calibration" . Indeed, in most industrial applications, due to uncertainties in the experimental system, the measured EC signal has to be calibrated with respect to a reference configuration. At this stage, we choose a first notch of 10 mm length, 0.93 mm depth and the opening is 0.1 mm. The EC probe is scanning a line along the length of the defect and finally simulated data and experimental data are normalized in order to fit the maximum value of the magnitude of the EC signal. The shape of the two signals are compared in Figure 6(a). In this figure, the real and the imaginary part of the signals are represented, the same signals are also displayed in the impedance plane diagram. As it is expected, the comparison shows a very small discrepancy between simulated data and experimental data due to, probably, local variations of the lift-off during the movement of the probe. The complex value of the normalization constant is fixed for all the following results of comparison. Figure 6(b) displays the EC signals when the probe is scanning perpendicularly to the defect. In the last experiment, let us consider two identical flaws separated by a gap of 3 mm (See Fig. 8(a)). The length of each defect is 10 mm, the opening is 0.1 mm and the depth is 0.76 mm. Figure 7(a) and 7(b) display two cartographies of the EC signals

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155

Figure 5. A scheme of the experimental set-up and an example of the EC probe including the GMR Sensor. Only one rectangular coil is activated for obtaining experimental data.

(a) the probe scans a line parallel to the notch

(b) the probe scans perpendicularly to the notch

Figure 6. A comparison of the EC signals of the first flaw.

collected when the probe is scanning above the flawed region. Figure 8(b) shows a slice view when the probe is moved along a line parallel to the X axis.

(a) Simulated data

(b) Experimental data

Figure 7. Two cartographies corresponding to the magnitude of the EC signals.

6. Conclusion The Volume Integral Method (VIM) and the Green’s dyadic formalism has been applied in order to compute the response of a magnetic sensor due to an arbitrary number of flaws in a stratified planar structure. The new functionalities which have been developed are able to compute the punctual value of the perturbed magnetic field above a flawed region. Two numerical approaches have been compared in order to show the validity of the new developments and some comparison results between simulated data and some experi-

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(a) The experimental set-up.

(b) the probe scans perpendicularly to the notch

Figure 8. A comparison if the EC signals due to two close flaws when the probe is scanning along a line parallel to the notch.

mental data confirm the validity of the global modeling approach. These developments will be available in the new version of the CIVA platform and some new developments are today already engaged for considering magnetic materials of constant permeability. References [1] R. F. Mostafavi and D. Mirshekar-Syahkal, "AC Fields Around Short Cracks in Metals Induced by Rectangular Coils", IEEE Transactions on Magnetics, 35(3), (1999), 2001-2006. [2] M. Ravan, S.H.H. Sadeghi and R. Moini, "Neural network approach for determination of fatigue crack depth profile in a metal, using alternating current field measurement data", IET Sci. Measurement Technology, 2(1), (2008), 32–38. [3] R. K. Amineh, M. Ravan, S. H. Sadeghi, and R. Moini, "Removal of Probe Liftoff Effects on Crack Detection and Sizing in Metals by the AC Field Measurement Technique", ", IEEE Transactions on Magnetics, 44(8), (2008), 2066–2073. [4] R. K. Amineha,1, M. Ravan, S.H. Sadeghi„ R. Moini, "Using AC field measurement data at an arbitrary liftoff distance to size long surface-breaking cracks in ferrous metals", NDT&E International, 41, (2008), 169–177. [5] B. Marchand, C. Zorni, J.M. Decitre and O. Casula, "Recent Developments of Eddy currents probes",ENDE 2009, to be published. [6] J.R. Bowler and L.D. Sabbagh and H.A. Sabbagh, "A Theoretical and Computational Model of Eddy Current Probes incorporating volume integral and Conjuguate Gradient Methods", IEEE Transactions on magnetics, 25(3), (1989), 2650–2664. [7] J.R. Bowler and S.A. Jenkins and L.D. Sabbagh and H.A. Sabbagh, "Eddy Current Probe Impedance due to a volumetric flaw", Journal of Applied Physics, 70(3), (1991), 1107–1114. [8] J.M. Decitre, D. Prémel and M. Lemistre, "3D Modelling of a Magneto-optic imager by a dyadic Green’s functions approach", Review of quantitative Nondestructive Evaluation, 22, ed. D.O. Thompson and D.E. Chimenti, IOP, (2003), 695-702. [9] T. Theodoulidis, G Pichenot , "Integration of tilted coil models in a volume integral method for realistic simulations of eddy current inspections", Electromagnetic Non-Destructive Evaluation (XI), Studies in Applied Electromagnetics and Mechanics, A. Tambourino, Y. Melikhov and L. Udpa, Amsterdam, IOS Press, 2008. [10] T.P. Theodoulidis and E.E. Kriezis, Impedance evaluation of rectangular coils for eddy current testing of planar media, NDT E International, 35(6), (2002), 407–414. [11] www-civa.cea.fr. [12] D. Prémel and A. Baussard, "Eddy current evaluation of three-dimensional flaws in flat conductive materials using a Bayesian approach, Inverse problems, 18(6), (2002), 1873–1889. [13] W.C. Chew,"Waves and fields in inhomogeneous media", IEEE Press (2nd edition), Piscataway,1995. [14] R.F. Harrington, "The method of moments in electromagnetics", Journal of Electromagnetic Waves and Applications, 1(3), (1987), 181–200.

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Automatic Detection and Identification of Image Quality Indicators in Radiograms Piotr BANIUKIEWICZ1 and Ryszard SIKORA Department of Electrical and Computer Engineering, Faculty of Electrical Engineering, West Pomeranian University of Technology, al. Piastow 17, 70-310 Szczecin, Poland

Abstract. In this paper the authors focus on detection of wire image quality indicators, which are widely applied in industrial radiography. Two algorithms for IQI detection are proposed. The first algorithm is intended for fast and rough detection of position of IQIs. It is based on evaluation of correlation between the radiographic image of IQI (together with a plastic case) and the fragments of the analyzed radiogram. The second algorithm uses the Radon transform applied to the region of interest (ROI) obtained from the first algorithm to extract the exact position of wires as well as information on visibility of each wire. Keywords. object recognition, radiography

Introduction Welding is a fabrication process that joins materials by causing coalescence. This is often done by melting two workpieces and joining them to make coalescence possible. Many different energy sources can be used for melting materials. The most popular are gas flame, electric arc, laser beam, friction and ultrasound. Welding can be done in many different environments, including open air, underwater and space. The chemical and physical processes that occur during melting and joining materials are very complicated and not fully understood. For example, metal cooling is a highly nonlinear physical process which proceeds simultaneously with chemical reactions. Those processes result in raising mechanical tensions in material as well as forming new chemical compounds in joint area (e.g. gases, slag, etc). Those undesired products are often the source of potential cracks and discontinuities in the joint. Additionally, the heat applied to the joint area in the process of welding causes overheating of the surrounding material and in the result the changes in its mechanical properties. Therefore, welding without proper precautions can be dangerous because of possible occurrence of defects and discontinuities in the weld. Due to high complications, the weld testing process mostly relies on the experience of human being. Defects and discontinuities in the weld can reduce the strength of the joint and can lead to a catastrophic failure. This is critical due to the application of a welding technique for joining stress-exposed parts such as ship hulls, skyscrapers, bridges and many more. There are many methods of nondestructive testing of the weld. Unfortunately, in most 1

Corresponding Author: Piotr BANIUKIEWICZ, West Pomeranian University of Technology, al Piastow 17, 70 310 Szczecin, Poland, email: [email protected]

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cases, the weld area is inhomogeneous, which is the result of processes which take place during metal cooling. This is a potential source of unwanted signals and disturbances that affect all methods of weld testing. Through the years the technology that utilizes penetrating rays has been the most important nondestructive testing (NDT) method. Fast and accurate x-ray converters that have been developed recently open new possibilities for x-ray applications and make this technique as flexible as never before. Digital radiography joins modern digital image processing algorithms with traditional x-ray testing method. Together with the fast development of digital radiography, there arise new nondestructive testing technologies based on it. One of the biggest problems of assuring the demanded quality of a product is the need of analyzing a large number of radiograms. In shipbuilding industry this number can reach even thousands. All radiograms must be analyzed by a qualified operator in order to find those welds which do not fulfill very restrictive safety norms. This process takes a lot of time and effort but it tends to be fully automated.The advanced computerized systems for radiogram analysis are still under development [1] and the decision taken by a human being is still considered as the most reliable and trustworthy. The process of radiogram analysis consists of a few stages which are strictly regulated by adequate norms. The first stage is always accepting or rejecting the radiogram according to its quality. Too dark, too bright, blurred or noised radiograms do not provide trustworthy information on internal structure of the specimen. In this paper the authors present an algorithm for detecting Image Quality Indicators (IQIs), which are commonly used for obtaining the quality of radiogram. This algorithm can be applied in the first stage of radiogram analysis process and it stands as a part of the automatic radiogram analysis system (ISARView) which is being developed by the authors. The aim of this procedure is only to find IQI in the radiogram and pass its position to other procedures implemented it the system for further analysis (e.g. accepting or rejecting radiogram because of its quality). The main procedure has been implemented in C++ and optimized for 64-bit environment.

1. Image Quality Indicators In radiography, one usually has a wide choice in the parameters of the radiographic technique. Most of them are regulated by norms but there is still margin for changes that can be done making the radiogram better or worse. For example, one has a choice of source-to-specimen distance, a choice of film type, a choice of film density, a choice of X-ray kilovoltage, X-rays or gamma-rays etc. The resulting radiograph therefore can vary between high quality and poor quality; quality in this case meaning the ability to detect small critical flaws such as cracks [2]. There are a lot of norms, both national and international, issued for particular applications as well as for a general purpose, giving advice or instructions on the choice of technique details, in order to ensure good quality radiographs. The usual method for measuring image quality in radiography is the use of Image Quality Indicators (IQIs). The quality of a radiographic image can be estimated in terms of three factors: • Image unsharpness • Image contrast • Image noise

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Figure 1. Exemplary image quality indicators of one wire (a). The effects of increasing geometric unsharpness in a duplex type IQI. A pair where the individual wire images are merged (c) and one can no longer see the two separate (b) wires stand for the unsharpness measure.

Using IQI it is possible to obtain all these three parameters and assess the quality of picture. There are four main types of IQIs. Those are: the wire type, the step/hole type, the hole-in-plaque type and the duplex wire type. Here, only the wire type and the duplex wire type are considered. A typical wire IQI contains six or seven straight wires of the same or similar material to the specimen having various diameters. The wires are held parallel to one another in a plastic mount with appropriate identification symbols. The double wire indicator is quite similar to wire type one. It consists of a series of pairs of wires of high density material (tungsten and platinum) where each pair of wires of diameter d is spaced at a distance d apart. Typical construction details and dimensions are specified in norms [3],exemplary indicators are depicted in Figure 1. The quality of the radiogram is defined based on the visibility of the wires. The duplex wire IQI measures only unsharpness as it is explained in Figure 1.

2. Problem statement The most important problem relating to IQI detection is that the low signal amplitude of the IQIs contributes to their poor visibility. Additionally, a typical radiogram consists of nonlinear trend that results from nonhomogeneity of the specimen and its non-uniform thickness. The amplitude of the trend signal is much greater than the intensities of particular wires. Thus, the process of the automatic determination of the

Figure 2. Exemplary real radiograms (fragment with IQI only) and corresponding averaged intensity profiles taken along weld line.

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quality of the radiogram needs special algorithms for accurate detection of IQIs. Exemplary real radiograms and intensity profiles are showed in Figure 2. The intensity profiles are averaged from dozens of lines taken along the weld line. As one can see, the signal from the wires is very poorly visible due to the low SNR. On the other hand, the plastic case form IQI gives a clear signal that is visible in intensity profile. This gives a possibility to detect position of IQI by means of image recognition algorithms.

3. The IQI detection process The process of detection of IQIs was divided into two steps. In the first stage only the presence and the position of the indicator are obtained whereas, the second step provides exact information on the position of particular wires. Thus, it is possible to evaluate the quality of the radiogram based on the visibility of wires in the wire type indicator or merging a pair of wires for the double wire indicator. Under fundamental initial assumptions for both algorithms lies norm [3] that regulates placement of IQI in the radiogram. In the case of welds, it is expected that IQIs are always located on the weld line almost perpendicular to it. Thus, the region of the analysis is limited to the weld line and a small surrounding area. The plastic case covering the wires in IQI is the best visible part of the whole indicator in the radiogram as well as in the intensity profile. This fact is used in the process of detection and localization of IQI. The algorithm works with averaged intensity profiles taken along the weld line. The position of IQI is obtained from a fusion of two methods commonly used in the pattern recognition. Those methods are: 1) to measure the dependence between sought pattern p and signal I using Pearson product-moment correlation coefficient and 2) evaluating phase correlation between Fourier transform of pattern p and Fourier transform of signal I. The pattern p is generated artificially as an average calculated from dozens of intensity profiles of IQIs obtained from various radiograms. The resulting waveform can be assumed as the best representative of IQI signal holding general features of that signal.The correlation coefficients were calculated between the pattern p and the window of size p sliding over the signal I with step of 1: ri =

n∑ Ii p − ∑ Ii ∑ p

n∑ I − ( ∑ Ii ) 2 i

2

n∑ p − ( ∑ p ) 2

2

(1)

where Ii stands for i-th position of the window in the signal I, n is the number of elements of p and Ii. The position of the maximum of function r is correlated with the position of IQI in the radiogram. In order to make the detection process more reliable the second criterion based on phase correlation has been proposed. In image processing, phase correlation is a method of image registration, and uses a fast frequency-domain approach to estimate the relative translative offset between two similar images. Here, this approach was applied to one-dimensional waveforms, namely intensity profile I and pattern p:

{

rp = F −1 e

(

i ϕ I −ϕ p

)

}

(2)

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Figure 3. Plots of Pearson product moment correlation coefficient r and phase correlation rp evaluated for intensity I (Figure 1b) and searched pattern p. Function R is fusion of r and rp clearly pointing position x of IQI (x=1182 for radiogram depicted in Figure 1b).

where F-1 stands for inverse Fourier transform and φI, φp are phases of Fourier transforms of I and p respectively. Because of the noise and the linear trend that are mostly present in radiographic images there is no clear maximum in either of the functions visible. Thus, the final criterion R was proposed as a fusion of correlation function r and phase correlation rp. All those functions are depicted in Figure 3. The position of the maximum of R stands for the position of IQI in the radiogram. In practice, the smallest element readily visible in the area under inspection is used to determine IQI sensitivity. Thus, the information on the presence or the position of IQI in the radiogram is not sufficient to draw any conclusions on its quality. One must know where exactly the wires are located and which of them are visible. For this reason the second algorithm has been developed. It uses information on location of IQI obtained from the first method to find positions of wires in the indicator. One of the well known methods commonly used for detecting straight lines in pictures is the use of Radon transform or related Hough transform. Using the Cartesian coordinate system to describe line integrals and projections, the IQI is represented by a two-dimensional function f(x, y) and each line integral by the (Θ, t) parameters. The equation of the line (being a particular wire in our case) is: t = x cos Θ + y sin Θ

(3)

The integral of line (3) is given as follows: PΘ (t ) =

∫

f ( x, y ) ds

(4)

( Θ , t ) line

what yields : PΘ (t ) =

∞ ∞

∫∫

f ( x, y )δ ( x cos Θ + y sin Θ − t ) dxdy

(5)

−∞ −∞

where Θ stands for the projection angle, t defines the position of the integral line on the projection and PΘ(t) is known as Radon transform of function f(x, y) [4]. The most important feature of Radon transform is amplifying straight lines to be found in pictures invariantly to their rotation angle. This makes it especially useful in the IQI detection process. Figure 4 shows Radon transform (sinogram) of the

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Figure 4. a) The IQI wires pattern generated artificially according to norms, b) Radon transform of part of the radiographic image and c) integrated intensity for Θ=6˚ as function of t. d)Results of detection of IQI position.

radiogram section that contains IQI. It is clearly visible on the line integral that peaks from the wires have been amplified in comparison to those original ones depicted in Figure 2. The detection algorithm of these peaks was realized in the same way as in the case of the first step described above. The correlation function r (1) is evaluated for all angles Θ from the sinogram and an artificially generated pattern representing the ideal IQI signal. The pattern is a sum of six Gaussian functions with increasing amplitudes (Fig. 4a). But now, unlike the previous case, the wires are under consideration and not the plastic case. Therefore, the maximum of r is found for two arguments of function PΘ(t) and it stands for the best matching of the whole artificial IQI pattern to the line integral for given Θ (Fig. 4c). The angle Θ is the rotation angle of the IQI relating to x axis whereas t is the radial coordinate of the first wire (beginning of the pattern) in the indicator. Having Θ and t, the first wire can be expressed as linear function y(x) defined for analyzed region of interest, which has been found by first algorithm, in the radiogram: π⎞ ⎛ y ( x ) = tan ⎜ Θ + ⎟ ( x − x0 − t cos ( Θ ) ) + y0 2⎠ ⎝

(6)

where x0 and y0 stand for the centre of the image. The result of the wires detection is presented in Figure 4d.

Conclusions Radiography is the most popular and well known method of nondestructive testing widely applied in industry. Information on the quality of radiographic picture is especially important in the case of the method of nondestructive testing. The algorithms for IQI detection presented in this paper have been applied in the automatic system of radiogram analysis (ISARView) in the first stage of the whole process of the analysis. Taking into consideration the fact that even thousands of radiographic pictures can be taken during manufacturing of e.g. a ship, the methods presented in this paper can significantly speed up the whole process of nondestructive testing in various branches of industry.

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Acknowledgments This work was conducted in a framework of the research project “The intelligent system for radiograms analysis”, supported by the Polish Ministry of Science and Higher Education. Grant no. NNR01003706/2009 (2009-2012).

References [1] European Commission sponsored project “Development of novel digital radiography technology. To facilitate the traditionally less research intensive inspection industry sector’ change from manual film radiography to automated digital”, contract No NMP2 C 2005 515746. [2] R. Halmshaw, T. Kowol, Image quality indicators in industrial radiography, IE NDT LTD technical materials [3] European norm EN 462 part 1:1994 [4] A. G. Rann, and A. I. Katsevich, The Radon Transform and Local Tomography, Boca Raton, FL: CRC Press, 1996.

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-164

Numerical Simulation of Acoustoelastic Effect in Pre-stressed Media Cuixiang PEI1 and Kazuyuki DEMACHI Department of Nuclear Engineering and Management, University of Tokyo, Tokyo 113-8656, Japan

Abstract: In this work, a code of finite element method is developed for numerical simulation of the acoustoelastic effect in pre stressed media. The possibility of assessing the stress status, by using the EMAT (electromagnetic acoustic transducer) receiver for precise measurement of LCR (refracted longitudinal) wave, is investigated. Besides that, the relationship between the polarization of transient Rayleigh wave and the state of stress is also predicted by simulation. Keywords: Ultrasonic NDE, Residual stress, Acoustoelastic effect, EMAT, Polarization

Introduction Ultrasonic NDE is one of the most promising methods for quantitative determination of residual stress in materials. And, most of ultrasonic methods for stress measurement are based on the effect of acoustoelasticity. The acoustoelastic effect, related to the change of ultrasonic wave speed and the polarization of Rayleigh wave, is a well established phenomenon that has been extensively reported in lots of literatures [1-4]. At present, the residual stress measurement by using acoustoelastic effect is mainly studied with experiment method. And simultaneously, the numerical simulation method can provide an another useful tool for the research of stress measurement with ultrasonic wave. In this work, the possibility of numerical simulation of acoustoelastic effect related to the stress status was investigated by using FEM method. Now in the practical application, the stress measurement using ultrasonic wave is mainly based on measuring the variation of ultrasonic wave velocity by time-of-flight. As the LCR wave is more sensitive to the in-plane stress and easy to yield, it is widely used in the subsurface stress measurement [9]. In this work, a kind of non-contact transducer named EMAT is proposed to precisely measure the acoustoelastic effect on LCR wave. There are some literatures have demonstrated that the polarization of Rayleigh wave related to the state of stress is usually more sensitive than the wave speed. The relationship between Rayleigh wave polarization and state of stress in homogeneous material was investigated by Junge et al[3]. However, in their analytical model, only a steady sinusoidal Rayleigh wave propagates in the material. Actually it is very difficult to generate a pure steady Rayleigh wave in the media, the Rayleigh wave in sinusoidal mode is usually interfered by the longitudinal and shear wave. In that case, it is 1 Email: [email protected]

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165

impossible to get an accurate estimation of the Rayleigh wave's polarization in the steady mode by experiments[5, 6]. However, it is possible to measure the polarization of the Rayleigh wave in a single pulse when it is separated from the longitudinal or shear wave. Therefore, it is very meaningful to investigate the polarization of the transient pulse Rayleigh wave related to the stress status.

1. Analytical model and numerical method 1.1 The acoustoelastic effect in solids An ultrasonic wave through a stressed body would give rise to further stresses, and the traditional theory of acoustoelasticity applied in the unstressed medium cannot be used here. Instead, based on the deformation process, Duquennoy et al. defined a theory of three states of a body, shown in Figure 1 [3, 4]. A solid body undergoes a series of deformations from a stress free state to a static deformation or a dynamic deformation. The position vector ξ defines the position of a point in the natural state of zero stress and zero strain. X defines the position of a point in the initial state when the body undergoes a static deformation due to residual stress during the manufacturing processes or due to the applied stresses. Similarly x defines the position in the final states when a dynamic deformation such as the ultrasonic wave through the body. The displacement of a point from one state to another can be described mathematically as:

u i (ξ )

X ξ ; u f (ξ ) x ξ ; u (ξ ) x X

uf

ui

Figure 1. Coordinates for material point in three states

Based on the three-state theory, the controlling equation of the acoustic wave in a solid with initial stress can be written as

(δ

i ˆ IK σ JL + C IJKL

) ∂∂X uX 2

J

γ

K

L

∂u I +f ∂t

i ) ρ 0 (1 ε NN

∂ 2u I ∂t 2

(1)

σ i is the Cauchy stress tensor in the initial state, ε i the initial strain tensor and ρ 0 the mass density in the natural state, γ is the acoustic damping coefficient, f is

where

the external force loading on the body. And for isotropic material the elastic constant can be expressed as

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C. Pei and K. Demachi / Numerical Simulation of Acoustoelastic Effect in Pre-Stressed Media

Cˆ IJKL

λδ IJ δ KL + μ (δ IK δ JL + δ ILδ JK ) + [( λ + v1 )δ IJ δ KL i i δ IJ ) + ( μ + v2 )(δ IK δ JL + δ ILδ JK )]ε NN + 2(λ + v2 )(ε IJi δ KL + ε KL i IK

i IL

i JK

(2)

i JL

+ 2( μ + v3 )(ε δ JL + ε δ JK + ε δ IL + ε δ IK ) where λ and μ are the well known Lame constants and vi (i 1, 2,3) are the third-order elastic constants (TOE constants). 1.2 Numerical simulation method for Ultrasonic wave According to FEM, Eq. (1) can be calculated by solving the discrete wave motion Eq. (3)

[ M ]{U&&} + [C ]{U& } + [ K ]{U } {F } (3) where [ M ] denotes the mass matrix, [C ] the damping matrix, [ K ] the stiffness matrix, {U } the nodal displacement and {F } the force vector. Eq. (3) is rearranged into the following equation by using the explicit integration method in time-domain [7]

⎧{U& }t +Δt = {U& }t −Δt − 2Δt [ M ]−1 [C ]{U& }t − 2Δt [ M ]−1 [ K ]{U }t + 2Δt [ M ]−1 {F }t ⎪ ⎨ {U& }t +Δt + {U& }t Δt ⎪{U }t +Δt = {U }t + ⎩ 2

(4)

1.3 Numerical method for EMAT Receiver A typical configuration for an EMAT receiver of acoustic waves in a test-piece is shown in Figure 2. It is usually composed of a static magnet and a set of coils (named pick-up coil). When the ultrasonic wave occurred in the test-piece under the EMAT receiver, the vibration by the ultrasonic wave would interact with the static magnetic flux density of the static magnet B0 to yield transient eddy current J e in the metal.

Je

σ e v × B0 , v is the velocity of a particle, σ e is the conductivity of the metal.

And a micro current would be induced by the electromagnetic induction effect. The magnetic flux density B0 of a permanent magnet can be calculated by equivalent magnetic charge approach [7]. The most direct way to calculate the pick-up signals of the EMAT receiver is to use Biot-Savart's law. According to Faraday's law, the electromotive signal of the pick-up coil is produced in the pick-up coil by the flux variation, N

∑∫

Ve

i =1 Si

∂B ef dS ∂t

(5)

f

where B e is the reaction magnetic flux density at a position of the pick-up coil produced by the transient eddy current, N is the number of turns of the pick-up coil, and Si is a surface surrounded by the wire of i-th pick-up coil. Substituting

B ef

∇ × A ef into Eq. (5) and applying Bio-Savat's law, we have,

C. Pei and K. Demachi / Numerical Simulation of Acoustoelastic Effect in Pre-Stressed Media

167

(6) where Γi is boundary of surface Si and

r denotes the distance from a current

source point in the conductor to a point in the pick-up coil. 2. Simulation of the Acoustoelastic effect in LCR wave 2.1 Numerical model In order to demonstrate the feasibility of this simulation method, the LCR wave’s acoustoelastic effect related to the in-plane stress was simulated in a three-dimension model, shown in Figure 2. As the piezoelectric (PZT) ultrasonic transducer is better as generator; and EMAT is better as detector. A PZT angle transducer was used to generate the LCR wave, and an EMAT probe was used to receive the time behavior of the LCR wave signal for different initial stresses σ x , uniaxially directed along the x axis. As shown in Table 1[6, 8], two kinds of material have been used here. Where, the sensitivity constant kc is defined as a relative change in wave speed per unit change in stress. When the longitudinal wave speed through a wedge is 2720 m/s, based on Snell’s law, the incidence angle θ w should be set at about 26o to generate the LCR wave in the model. 2.2 Numerical results and analysis To give a preliminary judgment of the validity of this method, the ultrasonic pulse was excited by one damped cycle of a 1 MHz sinusoidal force loading on a wedge with an angle. The simulation result of the ultrasonic wave field in a cross section at a given time is shown in Figure 3. The time behavior of the EMAT coil voltage is plotted in

z

y x

Figure 2. A pitch catch setup model in simulation Table 1 Material parameter of the model Material ρ / kg • m

3

−1  σe / S ⋅ m

λ / Pa

μ / Pa

v1 / Pa

v2 / Pa

v3 / Pa kc / MPa

Al Alloy D54s

2719.0

38.2E6

49.1E9

26.0E9

379.0E9

198.0E9

80.0E9

8.79E 5

Rail Steel

7800.0

1.1E6

115.8E9

79.9E9

36.0E9

266.0E9

178.5E9

1.214E 5

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C. Pei and K. Demachi / Numerical Simulation of Acoustoelastic Effect in Pre-Stressed Media

z x

Figure 3. Ultrasonic wave field excited by PZT

Figure 4. LCR wave received by EMAT

Figure 4. Compared to the Ultrasonic wave field, it can be seen that the first pulse in Figure 4 is the receiving signal of LCR wave. In Figure 5 and Figure 6, the close-up of the LCR wave signals for two initial stresses in Al Alloy and rail steel is provided. The acoustoelastic effect with a small phase delay induced by the stress can be observed. It can be seen that the variation in LCR wave speed due to acoustoelastic effect in rail steel is much smaller than that in Al alloy. The relative change in LCR wave speed for different initial stresses is simulated, shown in Figure 7. It can be seen that the simulation results show a very good agreement with the theoretical values.

Figure 5. Acoustoelastic effect in Al alloy

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169

Figure 6. Acoustoelastic effect in rail steel

Figure 7. Relative change of LCR wave’s speed in Al Alloy and rail steel

3. Simulation of the polarization of transient Rayleigh wave When Rayleigh wave travels across the surface of isotropic solids, the surface particles move in ellipses in planes normal to surface and parallel to the direction of the propagation. The polarization Π of Rayleigh wave is defined as the ratio between the maximum in-plane, and the maximum out-of-plane displacement components. As shown in Eq. (7), the sensitivity constant k p is defined as a relative change in polarization per unit change in stress

k p ⋅σ

ΔΠ

Π Π0 Π0

(7)

where, the subscript ‘0’ indicates the parameter at zero stress. In this work, the polarization of pulse Rayleigh wave excited by the PZT transducer was investigated by

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C. Pei and K. Demachi / Numerical Simulation of Acoustoelastic Effect in Pre-Stressed Media

FEM. In order to make a comparison with the results based on the theory of steady Rayleigh wave, three kinds of materials used in Junge’s paper were chosen here. As shown in Table 2,

k p' is the sensitivity constant in polarization of the Rayleigh wave

in steady mode[6]. Table 2 Material parameters Material ρ / kg • m

3

λ / Pa

μ / Pa

v1 / Pa

v2 / Pa

v3 / Pa

k 'p / MPa

Al Alloy D54s

2719.0

49.1E9

26.0E9

379.0E9

198.0E9

80.0E9

6.673E 5

Al (99.3%) Rail Steel

2710.0 7800.0

50.9E9 115.8E9

26.1E9 79.9E9

27.7E9 36.0E9

91.7E9 266.0E9

89.3E9 178.5E9

3.5809E 5 9.011E 6

The model is the same as in Figure 2. In order to yield a pure surface wave, the o

angel of incidence θ w is set at about 70 . The simulation result of Rayleigh wave field in a cross section at a given time is shown in Figure 8. Figure 9 presents the inplane and out-of-plane displacement components at point P on the surface of the unstressed Al alloy model. As can be seen, the two components have a phase-shift of π / 2 . The polarization of Rayleigh wave is presented in Figure 10.

z x

Fig. 8 Pulse Rayleigh wave field at a given time in Al alloy model

Figure 9. Rayleigh wave components at point P

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171

Figure 10. Rayleigh wave polarization at point P

Figure 11. Polarization of Rayleigh wave for different initial stresses in Al alloy model

Figure 11 presents the polarization of Rayleigh wave for different initial stresses in Al alloy model. It is observed that the polarization increases with increasing tension and decrease with increasing compression. Figure 12 presents the relative change of polarization for different initial uniaxial stresses σ x . It shows that the relative change in polarization of pulse Rayleigh wave is much larger than the reference values based on the theory of steady Rayleigh wave.

4. Conclusion In this paper, a numerical code is developed for numerical simulation of acoustoelatic effect in pre-stressed media. The possibility of assessing the stress status, by using the EMAT for precise measuring the LCR wave, was investigated. The numerical results showed a very good agreement with the theoretical values. Finally, the relationship between the polarization of transient Rayleigh wave to the state of stress was also predicted. The numerical results showed that the relative change in polarization of transient Rayleigh wave have a much larger value than that of steady Rayleigh wave due to the initial stress.

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Figure 12. Comparison of acoustoelastic effect of pulse Rayleigh wave with reference values of steady Rayleigh wave

Acknowledgement This work was supported by China Scholarship Council (CSC).

References [1] [2] [3] [4] [5] [6] [7] [8] [9]

Shamachary Sathish, Thomas J. Moarn, Residual stress measurement with focused acoustic wave, Materials Science and Engineering A 399 (2005), 84 91. Development of non contact stress measurement system during tensile testing using the electromagnetic acoustic transducer, NDT&E 39 (2006), 299 303. Michael Junge, Jianmin Qu, Relationship between Rayleigh wave polarization and state of stress, Ultrasonics 44 (2006), 233 237. Dequennoy M. Ouaftouh M., Ultrsonic evaluation of stresses in orthotropic materials using Rayleigh waves, NDT&E 32 (1999), 189 199. Shailesh Gokhale, Determination of applied stress in rails using the acoustoelastic effect of ultrasonic waves, Master's thesis, Texas A&M University, Dec. 2007. Michael Junge, Measurement of applied stress using polarization of Rayleigh waves. Master’s thesis, School of Civil and Environmental Engineering, Georgia Institute of Technology, August, 2003. Cuixiang Pei, Zhenmao Chen, Development of simulation method for EMAT signals and application to TBC inspection, Int. J. Appl. Electromagn. Mech., Vol.33, 2010. R.T. Smith, R. Stern, and R.W.B Stephens. Third order elastic module of polycrystalline metals from ultrasonic velocity measurements. Journal of Acoustical Society of American, 40(5):1002 1008, 1966. Don E. Bray, Wei Tang, Subsurface stress evaluation in steel plates and bars using the LCR ultrasonic wave, Nuclear Engineering and Design, 207:231 240, 2001.

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“BEMLAB” – Universal, Open source, Boundary Element Method library applied in Micro-Electro-Mechanical Systems1 Paweł WIELEBA a,2 and Jan SIKORA b,a a Department of Measurement and Diagnostic Systems, Electrotechnical Institute, ul. Po˙zaryskiego 28, 04-703 Warszawa, Poland b Department of Electronics, Lublin University of Technology, ul. Nadbystrzycka 38a, 20-618 Lublin, Poland Abstract. BEMLAB [1] is the open source project implementing Boundary Element Method (BEM) [2,3] comprehensively. BEMLAB binary packages and the source code are distributed under GNU LGPL (Lesser General Public License) license terms. The project provides universal library and the reference application, which is the easiest way for solving problems using BEM. The article presents example BEMLAB application in modelling comb capacitors used in Micro-ElectroMechanical Systems (MEMS). Finally capacitance will be calculated using BEM results. Particularly Asymptotic Boundary Conditions (ABC) will be used to model external space of the capacitor (the geometry of infinite half-lane) as an internal BEM problem. This approach will allow to calculate total capacitance with dispersed capacitance included. Results will be compared with the simplified model. Keywords. BEMLAB, BEM, Boundary Element Method, MEMS, Micro-ElectroMechanical Systems, Comb capacitors, Comb actuators, Asymptotic Boundary Conditions, Open source, Objectivity, Multi-threading

Introduction Micro Electro-Mechanical Systems (MEMS) are very small devices which dimensions vary in the range from 0.1μm to 0.1mm. They exchange energy either from electrical to other type for example mechanical, or mechanical to electrical. The most commonly known MEMS devices are ink-jet printers heads or accelerometers used in airbags. MEMS design process involves two modelling types – electrostatic and mechanical. This article incorporates electrostatic one and will concentrate on comb capacitors used in MEMS devices. The comb capacitors design stage problem requires to calculate capacitance C [4]. One method of calculating capacitance is usage of the simplified model based on the ideal parallel-plate capacitor. However this approach does not incorporate dispersed capacitances appearing in the corners and thus results are not precise enough. 1 http://bemlab.org/ 2 E-mail:

[email protected]

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P. Wieleba and J. Sikora / BEMLAB

The most precise modelling method which can be used for associating real physical properties and processes is the field method. Field method applied in electromechanics satisfies the Laplace equation. The most common numerical method of solving Laplace equation is the Finite Element Method (FEM) [5,6]. Many open source and commercial packages, which can be used to solve problems using FEM exist [7]. However this method is a domain one and requires discretization of the whole domain. While estimating condenser capacitance it is a worthless overhead. Therefore it is tempting to use the boundary method. However, there was no universal package which made it possible until BEMLAB [8,1] came into existence. Now it is possible and fairly easy.

1. BEMLAB – open source and objective project BEMLAB [1] is the open source project implementing Boundary Element Method (BEM) [2,3] comprehensively. BEMLAB binary packages and the source code are distributed under GNU LGPL (Lesser General Public License) license terms. The project provides universal library and the reference application, which is the easiest way for solving problems using BEM. There are also auxiliary programs provided to facilitate engineer’s tasks. A very important factor for the end user is the input/output data format, therefore the title library uses format compatible with Matlab M-files, Octave script files [9] and Scilab sci-files [10]. The project is objective and is developed using Unified Modeling Language. BEMLAB is implemented in C++. BEMLAB uses multi-threading (MT) to speed up calculations on multi-processor and multi-core platforms – nowadays CPUs have at least 2 cores. Threads introduced in C++0x specification are used. As an example GNU Compiler 4.4 or newer provides C++0x API.

2. Boundary Element Method BEM is the numerical method designed for solving physical problems described by Partial Differential Equations (PDE) but expressed as Boundary Integral Equation (BIE):  cϕ +

ϕ Γ

∂G dΓ = ∂n

 Γ

∂ϕ GdΓ + ∂n

 f GdΩ

(1)

Ω

where: Ω – problem domain; Γ – domain Ω boundary; ϕ – field function potential; G – Green function, a so-called fundamental solution; n – boundary element normal vector ∂ directed outwards the problem domain Ω; ∂n – normal derivative; f – domain (source) function; c – coefficient removing or restricting the singularity from the primitive function of PDE solution. Field modelling of comb capacitors requires Laplace PDE to be solved in the problem domain Ω: ∇2 ϕ(x) = 0

(2)

BIE (1) can be used to solve Laplace equation if proper Green function is applied. Green function (fundamental solution) for Laplace equation in 2D space is:

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G(R) =

1 1 ln 2π R

(3)

where R is the distance between the observation point for which the BIE equation is being set and the integration point of the element being integrated using the Gauss Quadrature.

3. Comb capacitors in Micro-Electro-Mechanical Systems Micro-Electro-Mechanical Systems use comb capacitors for detecting mechanical forces (conversion of mechanical energy into electrical) or for driving mechanical structures (conversion of electrical energy into mechanical). The structures using comb capacitors for driving mechanical parts are named comb actuators. An example MEMS device schema is presented in figure 1. It is a micro device of the scanning mirror, which consists of a mirror and four comb capacitor banks with two finger pairs each.

Figure 1. Scanning micro mirror with vertical comb capacitors.

Comb capacitors may have various shapes, dimensions and types. The article presents vertical comb capacitors with angular actuation. They are called Angular Vertical Comb (AVC) capacitors. Angular vertical comb capacitor finger in a tilted position was presented in figure 2 on the left side. Whereas on the right side it was presented in the rest position from the top perspective. Example dimensions of the AVC capacitor used Table 1. Angular Vertical Comb condenser fingers dimensions. Description

Symbol

Dimension [μm]

Finger length Finger width

l w

150 4

Finger height Gap between fingers

h d

40 3

Number of fingers in comb capacitor

N

12

for driving micro mirror are gathered in table 1 based on [11]. The capacitor is powered with the voltage of 20V, where potential of -10V is applied to one electrode and 10V to the second one.

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Figure 2. Angular Vertical Comb capacitor finger in a tilted position from the side perspective (left) and in a rest position from the top perspective (right).

4. Vertical Comb capacitor field model using Asymptotic Boundary Conditions In this section the problem for the AVC capacitor is defined and solved in order to calculate capacitance C. Field model is created for the boundary element method (BEM). All calculations are done using BEMLAB software. Firstly the geometry have to be defined. Here 2D model is considered. Gap between electrodes presented in figure 3 is to be modeled. The model was defined in the way so

Figure 3. Gap between AVC capacitor electrodes.

dispersed capacities are included in calculations. Due to the existence of the open space, an artificial boundary Γ(1t) have to be introduced. The gap is the domain of the problem

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marked by Ω(1) . Γ(1) is the boundary around the examined domain Ω(1) . Only finger halves are modeled because the whole structure of the comb capacitor is repeatable, as it consists of N finger pairs. Therefore boundary conditions of the second type ∂ϕ ∂n = 0 are applied on the left and right side of the presented model. The vertical dashed lines on the left and right of the figure 3 are placed in the center of particular fingers. The horizontal dashed line at the bottom of the figure also cuts particular fingers into two halves. Therefore zero boundary conditions of the second type (Neumann Boundary Conditions) ∂ϕ ∂n = 0 are also applied. Electrodes are conductors, therefore Dirichlet Boundary Conditions (boundary conditions of the first type) are applied on the boundary of electrodes. On the left finger (yellow) potential ϕ = −V is applied and on the right finger (right) potential ϕ = +V is applied. Almost all boundary conditions of the internal problem were defined. The only problematic boundary is Γ(1t) . The width of the Γ(1t) is a as marked at the figure 3 and is defined by d(t) length away from the electrodes. The Γ(1t) boundary placed in the infinity: d(t) → ∞

(4)

forms a half-lane beginning on the boundary of electrodes. Therefore special boundary conditions has to be introduced on Γ(1t) . Setting of zero Dirichlet Boundary Conditions is a one possibility, but the boundary should be moved far away towards the infinity: d(t)  a

(5)

which will increase the domain size and number of boundary elements used. Another one which will be used in the model, is using of Asymptotic Boundary Conditions (ABC) [12, chapter 4].

5. Asymptotic Boundary Conditions Asymptotic Boundary Conditions [12, pp. 52-73] for the half-lane are in the following form: 

∂ π ϕ=0 (6) + ∂y a where a – is the width of the half-lane. According to the BEMLAB software, the following notation has been used: ∂ϕ π =− ϕ+0 ∂y a ∂ϕ = mϕ + n ∂y

(7)

According to dimensions gathered in the table 1, parameters m and n of the ABCs (7) for the model presented in figure 2 are calculated below:

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w w +d+ =d+w =3+4=7 2 2 π π m = − = − = −0, 44879 a 7 a=

(8)

n=0

6. Field model calculations using BEMLAB When appropriate model definition is created, mesh of the geometry has to be generated. Figure 4 presented the boundary Γ(1) mesh of the model defined in figure 2. It was -3.5

-1.75

0

5.75

11.5

17.2

23 5

6

8

7

1

2

0

1.75

Z

Y

X

3.5

3

4

Figure 4. Boundary mesh of the AVC capacitor air gap between electrodes for the problem geometry defined in figure 3 with d(t) = 3.

generated using Gmsh software [13]. Corner geometric nodes has been marked with their numbers from 1 to 8. The modeled problem is 2D, therefore “z” coordinate equals 0. Boundary element method requires boundary elements normal vector n to be directed outwards the analyzed domain Ω. Therefore special attention has to be brought to the process of generating boundary mesh and after creating one its correctness has to be checked. BEMLAB software has the functionality of calculating normal vectors for any

−3.5

x

−1.5

1.5 3.5 0

y

20

23

Figure 5. Boundary elements normal vectors  n.

defined input mesh. Figure 5 presents normal vectors drawn against the generated mesh. As can be seen, blue normal vectors n are directed outwards the domain Ω(1) enclosed

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by the boundary domain Γ(1) marked with the solid line. The following BEMLAB command was used to calculate normal vectors of mesh defined in the input file defined by parameter -i: % obem_solve -i comb_cap_mesh.m -m 7 -o normal_vecs.m Results are written to the output file defined by the command parameter -o. The mesh and boundary conditions described in the previous section are gathered in one file: comb_cap_mesh.m Values of potential ϕ and its normal derivative ∂ϕ ∂n are the direct result of BEM. To start BEM calculations and obtain ϕ and ∂ϕ the following command has to be issued: ∂n % obem_solve -i comb_cap_mesh.m -m 1234 -o solution.m To visualize layout of potential along the domain Ω(1) , values of potential ϕ in internal nodes have to be calculated. This stage is optional and not required to calculate capacitance C, but is helpful to detect big calculation errors. This stage can be processed when potential ϕ and its normal derivative ∂ϕ ∂n are known on the whole boundary Γ. To proceed calculations the following shell command has to be issued: % obem_solve -i comb_cap_mesh.m -S solution.m -m 5 \\ -I comb_cap_internal_nodes.m -o internal_potential.m where -i – defines the input file with the input mesh with boundary conditions and material parameters (as in the previous paragraph), -S – defines the input file with the solution on the boundary (potential ϕ and its normal derivative ∂ϕ ∂n ), -I – defines the input file with the internal nodes coordinates, -o – defines the output file with calculated internal potential ϕ.

Figure 6. Layout of potential inside the AVC capacitors air gap defined in the figure 4.

Figure 6 presents the layout of calculated potential inside the air gap (domain Ω(1) ) calculated using the previous command.

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7. Capacitance calculations using BEM results Capacitance is calculated using the following relation:   C Q [F] = C= U V

(9)

where Q – charge gathered on one electrode, U – voltage between two electrodes of the capacitor. The charge Q can be calculated using the following integral:     ∂ϕ Q = σdΓ = Dn dΓ = εEn dΓ = ε dΓ (10) ∂n Γ

Γ

Γ

Γ

where σ – the surface charge density, Dn – electric displacement field , En – electric   field, ε – electric permittivity, and Dn = D  n . Finally the capacitance can be written in the following form:      1 ∂ϕ  (11) C =  ε dΓ ∂n  U Γ

Normal potential derivative ∂ϕ ∂n on the boundary is the direct result of BEM, therefore it can be directly inserted into equation (11). Figure 7 presents the layout of potential normal derivative ∂ϕ ∂n on the boundary of the right electrode (starting from node no. 1 to node no. 3 of mesh from figure 4). Potential normal derivative ∂ϕ ∂n , presented on the 12

potential normal derivative

10 8 6 4 2 0

0

10

20

30

40 element number

50

60

70

Figure 7. Layout of potential normal derivative on one electrode.

vertical axis, matches the number of the element presented on the horizontal axis. Firstly the charge Q was calculated for the half of one finger (as presented in the model): Q = 144.863 · ε

(12)

The integration was done using BEMLAB software by issuing the following command:

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% obem_solve -i int_electrode.m -m 8 integratedValue=[ 144.863 ]; where -i – defines the input file with geometry to be integrated and values of integrated function in the geometric nodes. Then the capacitance per unit length for half of one finger, using the field model with ABC applied, was calculated as follows: CI(half) =

Q 144.863 · ε = = 7.24 · ε [μF] U 20

(13)

= 7.24 · 10−6 · 8.854187817 · 10−12 = 64.104 [aF] The capacitance between two electrodes of one finger (2 halves) of the comb capacitor with the length l = 150 (the z dimension) and the gap width d = 3 is as follows: C (finger field) = 2 · (l − d) · CI = 2 · (150 − 3) · 64.104 = 18.847 [fF]

(14)

The total capacitance C (total) for the whole comb capacitor with N = 12 fingers is 2N times bigger than capacitance between two electrodes of one finger, as one finger has two sides (vertical). Therefore the total capacitance can be calculated as follows: C (total) = N · C (finger) = 12 · 18.847 = 226.164 [fF]

(15)

8. Vertical comb capacitor simplified model In the previous section calculations using the field model were proceeded. In this section the calculation of capacitance using the simplified model will be presented for the comparative purposes. The model for half of the finger as presented in previous section and on figure 2, consists of one parallel plate capacitor, which can be calculated as follows: C (finger simple) = ε

C h(l − d) 40(150 − 3) =ε =ε · 10−6 ε = 17.354 [fF] S d 3

(16)

9. Summary Universal, open source, objective and multi-threaded BEMLAB software can be successively used for modelling MEMS devices. Field modelling using boundary element method includes dispersed capacitance which occurs in comb capacitors, while simplified models not. The difference between calculated capacitance values using field and simplified model is 9%: C (finger field) = 1.09 C (finger simple)

(17)

BEMLAB software also allows three dimensional modelling for more complicated structures or in a tilted position, which cannot be modeled in 2D. BEMLAB input/output text file format implementation compatible with Matlab M-files, GNU Octave script files and Scilab .sci files makes cooperation with that software straight forward. Moreover engineering tools are provided to simplify cooperation with mesh formats provided by Gmsh [13] or Netgen [14].

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References [1] [2] [3] [4]

[5] [6] [7] [8] [9] [10] [11]

[12]

[13] [14]

P. Wieleba and J. Sikora: Open Source BEM Library, Advances in Engineering Software 40 (8), 564–569, 2009. L. C. Wrobel and M. H. Aliabadi: The boundary element method, vol. 1 and 2, Wiley, 2002. J. Sikora: Boundary Element Method for Impedance and Optical Tomography, Oficyna Wydawnicza Politechniki Warszawskiej, 2007. G. Of, M. Kaltenbacher and O. Steinbach: Fast multipole boundary element method for electrostatic field computations, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 28 (2), 304-319, 2009. O. C. Zienkiewicz and R. L. Taylor: The finite element method, vol. 1, Butterworth-Heinemann, 2000. R. Sikora: Teoria pola elektromagnetycznego, Wydawnictwa Naukowo-Techniczne, 1997. In Polish. J. Mackerle: Object-oriented programming in FEM and BEM: a bibliography (1990-2003), Advances in Engineering Software, 35, 325-336, 2004. BEMLAB homepage, http://bemlab.org/ Octave homepage: http://www.octave.org/ Scilab homepage: http://www.scilab.org/ W. Piyawattanametha, P. R. Patterson, D. Hah, H. Toshiyoshi and Ming C. Wu: A Surface and Bulk Micromachined Angular Vertical Combdrive for Scanning Micromirrors, IEEE Optical Fiber Communications Conference vol. 1, 251-253, 2003. S. Gratkowski: Asymptotyczne warunki brzegowe dla stacjonarnych zagadnie´n elektromagnetycznych w obszarach nieograniczonych – algorytmy metody elementów sko´nczonych, Wydawnictwo Uczelniane Zachodniopomorskiego Uniwersytetu Technologicznego w Szczecinie, 2009. In Polish. Gmsh homepage: http://geuz.org/gmsh/ Netgen homepage: http://www.hpfem.jku.at/netgen/

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-183

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Use of Half-Analytical Method for the Detection of Defects in Diet Pulses Hassane MOHELLEBIa,1, Ferroudja BOUALIa, Mouloud FELIACHIb Laboratoire de Génie Electrique, Université de Tizi-Ouzou, BP 17 RP, ALGERIA b IREENA Laboratory, IUT-CRTT, Nantes University, 44600 Saint-Nazaire, France a

Abstract. The present work concerns the development of pulsed eddy currents non destructive testing techniques applied to defects analysis. The impulse currents are produced with capacitor discharge bank [1], [2]. Coupled circuits method employed is based on the mutual inductances calculation [3] and associated to Kirchhoff laws yields to a real algebraic equation system which is solved at each time step. The model developed is used to the defects analysis of a cylindrical device [4]. Keywords. Half analytical method, eddy currents inspection, multi defects analysis , diet pulses.

Introduction The eddy currents sensors are used in diverse industrial domains which concern the evaluation of the physical properties of materials, the load dimensions, defect detection in a piece … etc. Pulsed eddy current (PEC) sensing is a new emerging technique and has gained considerable research attention in recent years [5]. Their first applications have been developed for the measure of material's thickness. The possibility to inject an important energy in short time with rich spectrum of low frequencies have induced an increase in use of them in the detection of multi-defects in pieces. This technique is used to inspect the riveted assembly, the slants and the objects of irregular surfaces, it holds the voltages of becoming the primary means of detecting corrosion in multilayered structures and to inspect, characterize the coatings [6],[8],[9],[10]. The present work deals with the study of the differential eddy currents sensor in pulsed diet by using a half-analytical method coupled with an equivalent electric circuit [2], [11]. The impulse currents technique is chosen instead of multi-frequency study which induces some difficulties when the number of frequencies exceeds four [7],[10]. In this case the use of impulse currents method present more advantages. The application of the method concerns the detection of two defects realized in a conducting cylinder scanned with differential probe. A cylinder with two layers is investigated too and a comparison with existing data is realized. 1

Corresponding Autor: Hassane MOHELLEBI, aLaboratoire de Génie Electrique, Université de Tizi Ouzou, BP 17 RP, ALGERIA ; e mail :[email protected]

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1. Coupled Circuits Method The half-analytical method used is the coupled circuits’ one based on a discretization of the inductor and load sections in (r,z) plane. The elementary sections constructed permit one to define elementary coils with associated elementary parameters (figure 1). Electrical parameters of the device as mutual and appropriate inductances exploits an integral calculus. Ub2

Ub1 Rb1

Lb1

Rb1n

Lb1n

Rb2

Rb1n

Lb2

Lb2n

Inductor

Rc1

Lc1

Rcm

L cm

Short-circuited load Figure 1. Coupled Circuits Model of device

Ub1, Ub2 are electric voltages of differential probe. Indices n and m are the maximum numbers of elementary coils of the inductor and short-circuited load. This process allows expressing the resistance of every elementary turn, the selfinductance and the mutual inductances between the various turns [12]. The electric equations of the load and the inductor are given by Eqs (1) and (2) as following: dI dI dI N m j i + ¦ M ij 0 = Ri I i + L + ¦ M ik k i dt dt dt j =1 k =1 j ≠i U

dI dI dI N m q k + ¦ M kq + ¦ M ki i = Rk I k + L k k dt dt dt q =1 i =1 q≠k

(1)

(2)

H. Mohellebi et al. / Use of Half-Analytical Method for the Detection of Defects in Diet Pulses

185

Ri, Li and Ii; Rk, Lk and Ik are the resistance, the constant inductance and the current. Indices i and k are related to load and inductor respectively. Mij: mutual inductance between both elements i and j of the load. Mik: mutual inductance between load and inductor elements. Ij: current in the element j of the load; Ik: current in the element k of the inductor. Mkq: mutual inductance between both elements k and q of the inductor; Mki: mutual inductance between the element k of the inductor and the element i of the load. Ik: current traversing the element k of the inductor. Iq: current traversing the element q of the inductor. 1.1. Model parameters computation Several methods have been proposed for the calculation of the parameters of the models. We can classify these in two big classes [4], [3]: - Methods based on the magnetic vector potential - Methods based on the mutual inductances calculation 1.1.1 Mutual inductance The mutual inductance betweentwo turns is given by [12]: M =μ

k2 =

ª 2 º 2 a .b «( − k ) K ( k ) − E( k )» k k ¬ ¼

(3)

4. a.b

(4)

(a + b)2 +h2

μ: Magnetic permeability; a: radius of the turn 1; b radius of the turn 2 ; h: distance between the two turns; K(k) and E(k) represent the elliptic integrals of first and second species respectively; M2

c

M1

a b

b

h

Figure 2. Distance between two turns

1.1.2 Appropriate inductance While joining the two turns, we get the expression of the self-inductance given by [12]:

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ª 8.a º L = μ a «ln − 1.75» ¬ Rc ¼

(5)

Rc : conductor radius 1.1.3. Resistance The turn resistance of elementary turn coil is given by Eq. (6): R=ρ

"

(6)

S

ρ : Material resistivity, S: Cross-section; " : Middle length of the turn. 2. Equivalent electrical circuit Model 2.1. Electrical Circuit Model

The relative electric model to the diet pulses is comprised of the equivalent circuit of the sensor-load coupled to the energizing circuit composed of a capacity and a resistance. The equivalent electric circuit of the system is given by the following Figure 3 [2]: Rext

ic(t)

Sensor system Lb

C

+

Vc(t) Rb

Figure 3. Equivalent electrical circuit

The electric equation modelling this system is given by Eq. (7): V C (t) − (Rext + Rb )ic (t) − Lb

iC (t ) = −C

dvc (t ) dt

dic (t ) =0 dt

(7)

(8)

Rb and Lb are the resistance and the inductance of the system load-inductor; Rext: external resistance; C: capacity.

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187

2.2. Analytical solution of electrical equation

The resolution of Eq. (7) combined with Eq. (8) yields to the following solution: ic ( t ) = C V0 (

With:

α1 =

α1 α2 )( eα t − eα t ) α1 − α 2 1

− (R ext + R eq ) −

(R

+ R eq ) − 4 2

ext

(9)

2

L eq

;

C

α2 =

2 Leq

− (Rext + Req ) +

(R

+ Req ) − 4 2

ext

Leq C

2 Leq

α 1 , α 2 are constants values. Initial time conditions v c (t = 0) = V0 , i c (t = 0) = 0 3. Application and Results The application considered in the present work is the one studied in [5]. It makes use of a differential probe used for the tubing inspection generator. The defects realized on the conducting cylinder are axisymmetric with resistivity W= 10-6[.m]. The physical and geometrical characteristics corresponding to differential probe are: coil width: 1.75*103 [m], distance between coils: 0.5*10-3, high in z direction: 0.75*10-3 [m], internal radius: 7.5*10-3 [m], magnetic permeability: 4X*10-7 [H/m] and the electrical conductivity: 5.59*10+7 [.m]-1(Figure 4). z J Inductor turns

+J

r

Cylindrical object

+J

J

Figure 4. Differential sensor with cylindrical tube inspection

3. 1 Analysis of the current response of several defects In this section we consider a healthy load (flawless) and loads with different types of defects (internal, in depth and external defect). The electrical circuit parameters used are: C = 10-7 F, Rext = 0.55 Y, Req= 1.6*10-3 Y, Leq= 1.0054*10-8 H, V0 = 1V.

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0.04

0.045 0.04

0.035

0.035

0.03

0.03

z [m ]

z [m ]

0.025 0.02

0.015

0.02 0.015

0.01

0.01

0.005 0 75

0.025

0.005

8

8.5

9 r[m]

9.5

10

0 7.5

10.5 x 10

8

0.04

0.04

0.035

0.035

0.03

0.03

0.025

0.025 z [m ]

z [m ]

9 r[m]

9.5

10

10.5 x 10

3

0.045

0.045

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0 7.5

8.5

3

8

8.5

9 r[m]

9.5

10

0 7.5

10.5 x 10

8

8.5

9 r[m]

3

9.5

10

10.5 x 10

3

Figure 5. Solving domain for a load presenting different defects

Figures 6 and Figure 7 represent the variation of the current for different defect types: 0.07

0.1

Healthy load Load with external defect Load with defect in depth Load with internal defect

0.06 0.05

0.06 Current[A ]

0.04 C urrent[A ]

Defect thickness 20% Defect thickness 40% Defect thickness 80%

0.08

0.03 0.02

0.04

0.02

0.01 0

0 -0.01

0

0.5

1

Time[s]

1.5

2

2.5 x 10

Figure 6. Variation of the current for different defect types

-0.02

0

0.5

1

1.5 Time[s]

7

2

2.5 x 10

7

Figure 7. Variation of the current with defect thickness

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While examining the results given in Figure 6 we notice that the current increase every time the sensor is near to the defect. The internal defect with maximum value of current Im constitute the more detected one because it is most near the sensor, then comes the defect in depth and finally the external defect. In Figure 7 there is represented the current response of the differential probe when considering different defect thickness (20%, 40%, 80%). In this case we notice that the parameter which varies more is the crest value of the current that increases progressively as the defect thickness increases. 3.2. Presence of two defects in the load In this application we consider a load with a combined defect, internal defect (40 % width) and an external defect (20 % width) (Figure 8). Figure 9 represents the variation of the differential current i(t) in the case of the load with an internal defect and in the case of the load with a combined defect, for C=10-6 F and R=0.2 Ω. 0.045

0.3

0.04

0.25

Combined defect Internal defect

0.035

0.2

C u rre n t[ A ]

0.03

z [m ]

0.025 0.02 0.015

0.15 0.1 0.05

T0

0.01

0

0.005 0 7.5

8

8.5

9 r[m]

9.5

10

10.5 x 10

-0.05

0

0.1

0.2

3

Figure 8. Solving domain with combined defects

0.3

0.4

0.5 0.6 Time[s]

0.7

0.8

0.9

1 x 10

6

Figure 9. Differential currents variations

Table 1. Internal and combined defects characteristics Im[A]

T0[s]

Internal defect

1.846 10

1

4.2129 10 7

Combined defect

2.075 10 1

4.4925 10 7

In Table 1, Im represents the maximum value of the current which results from difference between two currents turns; T0 is the time corresponding to current when it vanishes. According to the results presented in Figure 9, we note a difference between the differential currents i(t) in the case of the internal defect and the same unknown obtained in the case of the combined defect. The combined defect supplies amplitude Im with a time of passage by zero T0 more important. We can thus conclude that in spite of the internal defect is important; it does not hide the presence of the external defect.

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3.3. Case of a load presenting two layers

0.04

0.04

0.035

0.035

0.03

0.03

0.025

0.025 h a u t e u r[ m ]

h a u te u r[m ]

In this application we consider a load with two healthy layers and two layers with defects.

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0 7.5

8

8.5

9 rayon[m]

9.5

10

0 7.5

10.5 x 10

8

8.5

9 rayon[m]

3

9.5

10

10.5 x 10

3

Figure 11. Load with two layers with defects

Figure 10. Load with two healthy layers

The Figure 12 represents the variation of the induced electromotive force (e. m. f) u(t) in an elementary spire of the inductor for a flawless load, a load with defect, a load with two layers without defects and a load with two layers with defects. 0.12

1

load w th defect healthy load load w th two healthy layers load w th two layers with defects

0.08

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Figure 12. Induced e.m.f u(t) variation in an elementary coil of the inductor

Figure 13. Comparison with results given in [1]

This relative value of induced e.m.f (Figure 13) increases with increase of the layers number and also with the number of defects. These results with relative value variation with time allow to the same conclusion than the one given in [1].

4. Conclusion The half-analytic model developed in the current study is applied to the non destructive eddy current testing device. The study is undertaken in pulsed diet and a response of current is investigated for several defects nature of conducting tube. The case of the

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presence of two defects is considered and analysed. A cylinder with two layers is also studied and the results obtained are in a good agreement according to existing results. The model developed has shown its capability to analyse multiple defects in a conducting cylinder or multiple layers one with defect. The advantages of the model are less time consuming, which is very interesting compared to numerical models because in this case the air region was note discretized, and its capability to take into account of the movement of the sensor without changes in domain discretization.

References [1] N. Boucherou, M. Zergoug, A. Hammouda, G. Kamel, H. Boudjelal, A. Boutaghane, O. Bourdjam, Conducting materials evaluation using pulsed eddy currents, 18th French’s congress of mechanics, Grenoble (2007), pp. 27 31. [2] H. Mohellebi, F. Bouali, A. Diche Use of half analytical method for non destructive pulsed eddy current study, Colloquium of induction, April 13-14, Laghouat (2009), Algeria. [3] J. Ndinga, Modeling of magneto thermal phenomena : application to induction heating, PhD Thesis, I.N.P Grenoble, France 1987. [4] D. Delage, R. Ernst, Courant distribution prediction in axisymmetric inductor dedicated to MF and HF induction heating. RGE (1984), Vol. 4, no.84, pp.225 230. [5] J. L. Thomas, Simplified model of eddy current non destructive of generator tubing , Engineer Training report, CEA, France, 1998. [6] Young Kil Shin, Dong_Myung Choi, Young Joo Kim, Seung Seok Lee, Signal characteristics of differential pulsed eddy current sensors in the evaluation of plate thickness, NDT&E International (2009), pp. 215-221 [7] B. Maouche, R. Alkama, M. Feliachi, Semi analytical calculation of the impedance of a differential sensor for eddy current non destructive testing, NDT&E International, (2009), pp. 573 580 [8] Y. BinFeng, L. FeiLu, H. Dan, Reseach on edge identification of a defect using pulsed eddy current based on principal component analysis, NDT&E International, (2007), .pp. 294 299. [9] T. Chen, G. Y. Tian, A. Sophian, P. W. Que, Feature extraction and selection for defect classification of pulsed eddy current NDT, NDT&E International, (2008), pp. 467 476. [10] Deeds W.E., A comparison of multiple frequency and pulsed eddy current techniques, Proc. of the 5th annual review of progress in quantitative NDE, Lajolla, USA (1978), pp. 117 1 19. Fields, Leuven Belgium (1994), 18 20. [11] M. Abdellah, A. Hammel, A. Zaoui, H. Mohellebi, Study of the feeding mode effect on the linear induction launcher (LIL) performances, in Proc. Wseas Transactions On Systems, (2005) .Issue 10, Vol. 4, pp. 1798 1804. [12] F. Gardiol, Traité électricité, Electromagntics, Volume III, Presse Polytechniques et Universitaires Romandes, Suisse, 1996.

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-192

Imperialist Competitive Algorithm Applied to Eddy Current Nondestructive Evaluation Ammar HAMELa,1 Hassane MOHELLEBIb and Mouloud FELIACHIc Electrical Engineering Laboratory, Departement of Electrical Engineering, University of Béjaïa, Algeria [email protected] b Electrical Engineering Laboratory, Departement of Electrical Engineering, University of Tizi-Ouzou, Algeria b [email protected] d [email protected] c IREENA Laboratory, IUT of Saint-Nazaire, University of Nantes, France [email protected] a

Abstract. The imperialist competitive algorithm (ICA) is a new global search strategy inspired by the socio political process of Imperialistic competition. ICA has higher performances such as faster convergence and better global minimum achievement [1]. Considering its undeniable effectiveness, its limitations and applicability in various fields, ICA is currently explored. In this paper we adopt ICA to deal with the inverse problem applied in eddy current non destructive evaluation. We present test results and a comparison between ICA and the particle swarm optimisation algorithm (PSO). Keywords. Non destructive evaluation, eddy currents, inverse problem, imperialist competitive algorithm.

Introduction To improve time necessary to the inversion in eddy current non-destructive evaluation, the specialists tackle the problem by considering two principal aspects, in the event the development of direct models reliable and applicable to cases of complex geometry and especially which are fast on the one hand, and the implementation and adaptation of sure and fast algorithms of inversion on the other hand. In this work we are interested rather in the second aspect in which the methods which are already used can be shared in two groups. The first group includes what is called the non-phenomenological methods and which are based on the techniques of signal processing [1], [2]. If they are fast, these methods have nevertheless a major disadvantage which is the need for an enormous data base of signals and various forms with a very good precision. Increasing interest has been granted in recent years, with the use of stochastic optimization methods that guarantee the convergence to the global optimum of the function to optimize. Several algorithms based on these methods are used in eddy current nondestructive evaluation, namely genetic algorithms, simulated annealing, taboo search and recently particle swarm optimization… [3]- [5]

1

Ammar HAMEL, Electrical Engineering Laboratory, Department of Electrical Engineering, University of Béjaïa, Algeria [email protected].

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The main contribution of this paper is an extension to eddy current non-destructive evaluation of a new inversion algorithm called imperialist competitive algorithm (ICA). ICA is an iterative evolutionary computation technique and a socio-politically motivated global search strategy that has recently been introduced for dealing with different optimization tasks. The proposed method is applied to a simple axisymmetrical conducting tube with a groove made arbitrarily. The aim is to reconstruct sizes of the groove by combining the finite element method for the computation of eddy current with the optimization algorithm in the inverse process.

1. 2D Electromagnetic equation Starting from an impedance measurement, the aim is to reconstitute the profile of an axi-symmetrical groove practiced inside an aluminum tube inspected by a differential probe. The solution is obtained by using a forward model based on the finite element method and ICA algorithm to solve the inverse problem. The axisymmetric diffusion equation can be expressed in variational terms by the energy functional [6], 2 2 ! 1 1   A  j 2 

F  " r  A   A J s . A  2 .r.dr.dz z  2  2   r r  R   

(1)

The energy terms corresponding to the magnetic field, eddy current and source current are represented by the first, second and third terms, respectively, of the integrand. The impedance of a filamentary circular loop of radius ri can be calculated from the magnetic vector potential Ai at ri and the value of the impressed current I s in the loop as follows: # j.2 .ri . Ai E t Zi    Is Is Is

(2)

Hence, the total impedance of the circular coil whose cross section is discretized into N triangular elements is given by Z

j.2 .J s N j.2 .N s N %  r A . $ ci ci i $ rci .% i .Aci Is I s2 i 1 i 1

(3)

Where N s : turn density [turns / m 2 ] , % i : area of i-th element, rci , Aci : central values of r , A in i-th element. So the total impedance of a differential probe can be obtained by summing the impedance of each coil of the differential probe.

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2. Imperialist competitive algorithm Like other evolutionary techniques, ICA starts with an initial population. Population individuals called countries are divided into two types: colonies and imperialists that all together form some empires. Imperialistic competition among these empires forms the basis of ICA. During this competition, weak empires collapse and powerful ones take possession of their colonies. Imperialistic competition hopefully converges to a state in which there is only one empire and its colonies are in the same position and have the same cost as the imperialist. The pseudo code of Imperialist competitive algorithm is as follows [7]: & & & & & & & & &

Select some random points on the function and initialize the empires. Move the colonies toward their relevant imperialist (Assimilation). Randomly change the position of some colonies (Revolution). If there is a colony in an empire which has lower cost than the imperialist, exchange the positions of that colony and the imperialist. Unite the similar empires. Compute the total cost of all empires. Pick the weakest colony (colonies) from the weakest empires and give it (them) to one of the empires (Imperialistic competition). Eliminate the powerless empires. If stop conditions satisfied, stop, if not go to second point.

To start the optimization algorithm we generate the initial population of size N pop . We select N imp of the most powerful countries to form the empires. The remaining N col of the population will be the colonies each of which belongs to an empire. Then we have two types of countries: imperialist and colony. To form the initial empires, we divide the colonies among imperialists based on their power. That is the initial number of colonies of an empire should be proportionate to its power. Figure 1 shows an example of an initial population of each empire.

Imperialist 1 Colony 1 Imperialist 2 Colony 2 Imperialist 3 Colony 3 Imperialist n Colony n

Figure 1. Initial empires.

The movement of colonies toward their relevant imperialist is shown in figure 2 in which the colony moves toward the imperialist by x units. In this movement,  and x are random numbers with uniform distribution as illustrated in formula (4) and d is the distance between colony and the imperialist.

A. Hamel et al. / ICA Applied to Eddy Current Nondestructive Evaluation

x ~ U 0,  d , ' ~ U  ,  

195

(4)

Where and  are parameters that modify the area that colonies randomly search around the imperialist. In our implementation and  are considered as 2 and 0.5 (Radian) respectively. Imperialist New position of colony

x

'

d

Colony

Figure 2. Movement of colonies toward imperialist.

In imperialistic competition, all empires try to take possession of colonies of other empires and control them. Powerless empires will collapse in the imperialistic competition and their colonies will be divided among other empires. In modelling collapse mechanism, different criteria can be defined for considering an empire powerless. In our implementation we assume an empire collapsed and eliminate it when it loses all of its colonies. Convergence is obtained when all the empires except the most powerful one will collapse and all the colonies will be under the control of this unique empire. 2.1. Validation with test functions ICA was implemented and then tested with some benchmark functions. The results which we give hereafter are those found with the function F which is written [7]: F  x  sin 4 x   1.1  sin 2 y 

(5)

Figure 3 shows a 3D plot of the function F . The global minimum of this function is in the interval 0 ( x ( 10 , 0 ( y ( 10 , is located in x, y   9.039,8.668 and has the cost of 18.5547 .

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A. Hamel et al. / ICA Applied to Eddy Current Nondestructive Evaluation

Figure 3. 3D plot of the function

F.

The initial population is of 30 countries. We choose 4 of the best countries to form the imperialists which are shown by stars marks in different colors while the colonies by round points in the same color as the imperialist. Figures 4 (a, b, c, d) show the countries at iterations 5, 10 and 20 (convergence). We can see that at iteration 5, the imperialists are located at local minima of the function and one of them has reached to the global minimum. At iteration 10, only two imperialists are remained and the others have collapsed. At iteration 20, all the imperialists have collapsed except one and colonies are in the same position as the imperialist. Due to the mutation at last iteration, some of the colonies are in different position. 9

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Figure 4. Initial empires (a). Empires at iteration 5 (b). Empires at iteration 10 (c) Empires at iteration 20 (d).

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We also applied Particle Swarm Optimization (PSO) algorithm to the function F [8]. To make a comparison we choose a population of 30 particles. Both global and local attraction parameters are equal to 1.4. Figure 5 shows average and best cost of population versus iterations obtained with PSO and ICA. 20

5 0 -5 -10 -15 -18.5547

-15 -17 -18.5547

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Figure 5. Mean and minimum cost versus iterations by PSO (a) and ICA (b).

Results show that with ICA the convergence is reached more quickly than with PSO. Indeed with PSO convergence is obtained after approximately 240 iterations whereas with ICA it is obtained after 20 iterations. We noted that the execution time of iteration is practically the same one for both algorithms. Consequently, ICA finds the global minimum successfully.

3. Application and results The problem geometry is that studied in [9]. A differential probe is used to scan a conducting tube (aluminum) having an electrical conductivity  c  1M )s / m* . The geometrical and electrical data of the eddy current differential probe is as follows: height of a coil according to z: 0.75e-3 m, inner radius of a coil: 7.75e-3 m, outer radius of a coil: 8.5e-3 m, vertical distance between the coils: 0.5e-3 m, number of turns of a coil: 70. The probe is supplied by a current with intensity of 5mA and a frequency of 100kHz . The impedance measured when the medium of the coil is opposite the lower edge of the groove is Z m  (0.55 j1.45)+ . The inversion is based on an iterative approach that employs a direct finite element model to simulate the fundamental physical process, as shown in figure 5. The inversion algorithm starts with an initial estimate of the groove profile and then determines the signal by solving a finite element direct problem. The error between the measured and the calculated signals is minimized iteratively by updating the groove parameters by keeping the best profile of the previous iteration. When the error is below a threshold, the profile determined is the desired solution.

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Measured signal

Z m 

Calculated signal

Initial groove profile

Z c 

Forward model

Z m Z c  , -

Yes

Desired solution

No

Update groove profile

Figure 6. Inversion principle method

Figures 7 (a) and (b) illustrate the evolution of the groove parameters obtained by PSO and ICA respectively. By PSO, convergence is obtained after 124 iterations. The value of the height and the depth of the groove are h  3.98mm and p  0.508mm respectively. On the other hand, by ICA, convergence is practically obtained with 22 iterations and then the value of the height and the depth of the groove are h  3,97 mm and p  0,509mm respectively. In order to make comparison we used the same number of particles in PSO as of countries in ICA i.e.30. We noted that the execution time of iteration is the same one for both algorithms. Consequently, this enables us to conclude that ICA converges more quickly than PSO algorithm. Nevertheless, with regard to the precision of the results, PSO proves to be slightly better than ICA. -3

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Figure 7. Groove parameters by PSO (a) and ICA (b).

4. Conclusion

The method proposed in this paper, Imperialist Competitive Algorithm (ICA) uses an evolutionary algorithm in order to inverse eddy current non-destructive evaluation signals. The aim is to reconstitute the profile of an axi-symmetrical groove. The method uses a finite-elements forward model to simulate the physical process and Imperialist Competitive Algorithm to solve the inverse problem. This evolutionary optimization strategy has shown great performance in both convergence rate and global optima achievement. Indeed, from the experimental results, it can be seen that the ICA method outperforms the PSO one in terms of speed convergence. However, PSO remains a method which gives results with a better precision. In continuing this work, the proposed algorithm could be extended to reconstitute complex profiles.

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References [1] S. Hoole, S. Subramaniam, R. Saldanha, and J. Coulomb, Inverse Problem Methodology and Finite Elements in the Identification of Cracks, Sources, Materials, and their Geometry in Inaccessible Locations, IEEE Trans. Magn., vol. 27 (1991), pp. 3433 3443. [2] Y. Li, L. Udpa, and S.S. Udpa, Three Dimensional Defect Reconstruction From Eddy Current NDE Signals Using a Genetic Local Search Algorithm, IEEE Trans. Magn., vol 40, No. 2 (2004), pp. 410 417. [3] M. Rebican, Z. Chen, N. Yusa, L. Janousek, and K. Miya, Shape Reconstruction of Multiple Cracks From ECT Signals by Means of a Stochastic Method, IEEE Trans. Magn., vol 42, No. 4, (2006), pp 1079 1082. [4] M. Cacciola, S. Calcagno, F. C. Morabito, and M. Versaci, Swarm Optimization for Imaging of corrosion by impedance measurements in Eddy Current Test, IEEE Trans. Magn., vol. 43, No. 4, (2007), pp 1853 1856. [5] A. Hamel, H. Mohellebi, M. Feliachi and F. Hocini, Particle Swarm Optimization for Reconstitution of Two Dimensional Groove Profiles in Non Destructive Evaluation, ISEF 2009 XIV International Symposium on Electromagnetic Fields in Mechatronics, No. 4, September 10 12, Arras, France, (2009), pp. 1079 1082. [6] O.C.Zienkiewicz and R.L.Taylor, The Finite Element Method, 4th ed., McGraw-Hill, 1989. [7] E. Atashpaz Gargari, C. Lucas, Imperialist Competitive Algorithm : An Algorithm for Optimization Inspired by Imperialistic Competition, IEEE Congress on Evolutionary Computation, Singapore ,( 2007), pp 4661 4667. [8] R. C. Eberhart and J. Kennedy, A New Optimizer Using Particle Swarm Theory, proc. Sixth International Symposium on Micro Machine and Human Science (Nagoya, Japon), IEEE Service Center, Piscataway, NJ (1995), pp. 39 43. [9] J.L Thomas, Modélisation du Contrôle Non Destructif par Courants de Foucault des Générateurs de Vapeur, Rapport de Stage 3ème année de cycle d’ingénieur, CEA, France, 1998.

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Transducers and Techniques

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Pulsed ECT Method for Evaluation of Pipe Wall-thinning of Nuclear Power Plants using Magnetic Sensor Shejuan XIEa, Toshihiro YAMAMOTOb, Toshiyuki TAKAGIa,1 and Tetsuya UCHIMOTOa a Institute of Fluid Science, Tohoku University, Japan b Japan Power Engineering and Inspection Corporation, Japan

Abstract. In nuclear power plants, there may happen local wall-thinning on the inner surface of a pipe due to the flow of coolant flowing inside the pipe. Pulsed eddy current testing (pulsed ECT) technology is developed in recent years. Because of its rich frequency components and applicability of large electric current, a pulsed ECT method may show promising capability of detecting and evaluating the defect in the deep region of the material. The aim of this study is to discuss the feasibility of detection and evaluation of local wall-thinning of the bottom surface in one thick layer and also in the lower layer of two-layer structure pipe using a pulsed ECT method. Concerning the large thickness of the specimen, a high sensitive flux gate (FG) sensor has been employed and the corresponding differential exciting mode has been developed to efficiently apply the FG sensor. Experimental results show that this FG sensor combined with differential exciting mode could detect a very small defect that is located in a thick specimen while which could not be detected by Hall sensor. Keywords. local wall-thinning, pulsed ECT, differential exciting mode, FG sensor

Introduction In nuclear power plants, there may happen local wall-thinning on the inner surface of a pipe due to of the flow of coolant flowing inside the pipe (flow accelerated corrosion (FAC)). Normally, the thickness of the pipe is very large. In addition, in Japan, there is a special concern about local wall-thinning under an enforcement plate that covers the outside of a pipe where a branch pipe is connected to a main pipe. Because the enforcement plate and the pipe wall form two layers of the metal plate, also the existence of thick insulators outside the pipe, these make it very difficult to inspect the inside of the pipe by ultrasonic testing method. Pulsed eddy current testing (pulsed ECT) technology is one of the methods developed in recent years [1, 2]. Because of its un-necessity of contact between the probe and the inspected specimen, also its rich frequency components and applicability of large electric current [3-5], pulsed ECT method may show promising capability of detecting and evaluating the defect in the deep region of the material with lift-off. The aim of this study is to discuss the feasibility of detection and evaluation of local wall-thinning of the bottom surface in

1

Corresponding Author: Toshiyuki TAKAGI. Katahiri 2-1-1, Aoba-ku, Sendai 980-8577, Japan; E-mail: [email protected]

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one thick layer and also in the lower layer of two-layer structure pipe using a pulsed ECT method with small lift-off. When the specimen is rather thick, low frequency is preferred due to the skin effect phenomenon. It has been pointed out that the sensitivity of pulsed ECT technique can be greatly enhanced when magnetic sensors are applied instead of pick-up coils for picking up the field. The enhancement can especially be beneficial when deeply buried defects are of the prime concern [6]. There is a family of magnetic field sensors, such as, SQUID (Superconducting Quantum Interference Device), FG (flux gate) sensors, AMR (anisotropic magnetoresistive), GMR (giant magneto-resistive) and Hall devices [6]. As we know, SQUID possesses the highest sensitivity but its use is still limited due to practicality and some cost-related reasons [7]. Hall sensor is not a bad choice when the specimen is not very thick and also the defect is not very small, but for the small defect detection in a thick specimen Hall sensor is not preferred due to its relative big noise level (i.e. poor resolution, according to the reference [6] and also the experience of the author). Thus FG, AMR and GMR sensors are good candidates for the small defect detection in rather thick specimen. In this study, FG sensor was employed for the local wallthinning detection in large diameter pipes. Concerning the characteristics of FG sensor, of course, high sensitivity and high resolution are its obvious merits, but at the same time, small measurement range is its inherent demerit, normally inside several Gauss. To overcome the trade off of high sensitivity and small measurement range, in this study, a differential exciting mode has been developed and the corresponding two identical exciting pancake coils have been designed. 1. Duty analysis of square wave pulse exciting signal Figure 1 shows the ideal square wave pulse. The corresponding FS representation in trigonometric series can be given by equation (1),

u (t ) =

d N 1 1 + ∑ [ sin(nω d ) * cos(nωt ) + (1 − cos(nω d )) *sin( nω t )] T n 1 nπ nπ

(1)

Where, (1/nπ)×sin(nωd)=an, (1/nπ) × (1-cos(nωd))=bn, d denotes pulse width (the duration of exciting pulse) and T denotes pulse period, thus duty τ can be expressed by d/T (i.e. τ= d/T ). The fundamental angular frequency ω=2π/T, n denotes the harmonic order and N is the number of summation terms (in case of ideal square wave pulse, N is positive infinite).

Figure 1. Ideal square wave pulse

The amplitude of n-th harmonic frequency could be written by equation (2),

S. Xie et al. / Pulsed ECT Method for Evaluation of Pipe Wall-Thinning of Nuclear Power Plants

An = an 2 + bn 2 =

2 * 1 − cos(nω d ) nπ

205

(2)

So, when duty is τ, the amplitude of n-th harmonic frequency is,

An ,τ =

2 2 * 1 − cos(nω d ) = * 1 − cos(2nπτ ) nπ nπ

(3)

When duty is 1-τ, the amplitude of n-th harmonic frequency is,

An ,1−τ =

2 2 * 1 − cos(nω (T − d )) = * 1 − cos(2 nπτ ) nπ nπ

(4)

From the above equation (3) and (4), we can see that when the duty of two square wave pulse signals is complementary to 1, their spectrum distribution should be completely the same only except the spectrum of DC component. FFT was applied to the square wave pulse under condition of different duties (0.1, 0.2,……, 0.9), then the energy (here amplitude was considered as energy) percentage of the fundamental frequency, which means energy of fundamental frequency divided by the energy of all the harmonic frequencies (except DC component) has been obtained and shown in Figure 2.

Figure 2. Energy percentage of the fundamental frequency

From Figure 2 we can see that when duty is 50%, the energy percentage of fundamental frequency is the biggest. Therefore, if the defect is located on the subsurface of a thick specimen, big pulse period (which means low fundamental frequency) and 50% duty are preferred because more information from deep position of the specimen can be expected by low frequency. However, if the defect is located on the surface of the specimen, short pulse period combined with small duty (e.g. 10% duty) is more suitable in pulsed ECT technique. In this study, 50% duty of pulse was applied to detect the local wall-thinning on the bottom side of pipes. 2. Pulsed ECT system 2.1. Specimens To simulate the local wall-thinning on the bottom side of one layer thick pipe, three AISI316 austenitic stainless steel flat plates with a slot defect were prepared in our experiments. The size of the three plates is the same, 300mm in length, 100mm in

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width and 20mm in thickness. A rectangular slot was arranged along the center line of the bottom side of the plate in the shorter direction. The size of the slot defect (width×depth) is 20×10, 10×10 or 10×5 (mm), respectively. The slot defect is to be detected from the top surface of the plate. The specimen is shown in Figure 3.

Figure 3. One plate specimen with a slot defect simulating local wall-thinning in one layer thick pipe

To simulate the local wall-thinning on the bottom side of a pipe which is covered by an enforcement plate, we have prepared two AISI316 austenitic stainless steel flat plates for our experiments. The size of the two plates is the same, 500mm in length, 300mm in width and 8mm in thickness. One plate is placed on the top of the other. A rectangular slot has been arranged along the center line of the bottom side of the lower plate in the shorter direction. The width of the slot is 10mm, and the depth is 1, 3 or 5mm, respectively. The slot is to be detected from the top surface of the upper plate. The specimen is shown in Figure 4.

Figure 4. Double-plate specimen with a slot defect simulating local wall-thinning in two layer pipes

2.2. Experiment setup The pulsed ECT experiment system we established consists of a function generator (WF1945, NF), a power amplifier (BP4610, NF), a scanning stage, an AD board and a PC etc. In the experiments, a square wave pulse was generated from the function generator and then amplified by the power amplifier by which the output current could be controlled instead of the output voltage. Then the amplified current signal of the square wave pulse was applied to the exciting coils as the exciting signal. A magnetic sensor is supposed to be the pick-up sensor for picking up the magnetic field. The pulsed ECT experiment setup is shown in Figure 5. 2.3. Pick-up sensor As mentioned in the Introduction part, because of demerit of SQUID and Hall device, in this study a TMF-FG sensor, one kind of FG sensor, was employed to detect local wall-thinning in large diameter pipes. The manufacturer of this FG sensor is Canon, sensitivity 1V/G, voltage source DC 5V, offset 2.5V, measurement range about from 2.5G to 2.5G and resolution is about 1mG according to the manual. The circuit board of sensor and its output property are shown in Figure 6(a) and Figure 6(b), respectively. From Figure 6(a) we could see that on the circuit board there are two sensors which can measure the magnetic field of two directions (measuring direction is parallel to the length direction of the sensor). In experiments, one sensor or two sensors can be used at

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one time according to the experiment request. Figure 6(b) shows that the output has good linear property to external magnetic field within the measurement range.

Figure 5. Pulsed ECT experiment setup

(a) TMF-FG sensor

(b) Output property

Figure 6. TMF-FG sensor and its output property

2.4. Exciting and pick-up mode Generally speaking, as far as the magnetic sensor is concerned, there is trade off between the sensitivity and the measurement range, i.e. low sensitivity with large measurement range while high sensitivity with small measurement range. For FG sensor, small measurement range is its inherent demerit. To overcome this problem, in this study, a differential exciting mode has been developed and shown in Figure 7(a). There are two almost identical exciting coils, coil 1 and coil 2, the parameters of which are shown in Table 1. Reverse exciting signal has been applied to the two exciting coils and FG sensor has been located at center of the two coils (see Figure 7(b)). It has been pointed out that the ratio between the variations of the perturbed field to the unperturbed field is maximized along the direction which is perpendicular to the coil circle plane [7]. So in experiments, the magnetic field of vertical direction (perpendicular to the coil circle plane and surface of specimen) was measured by FG sensor. The distance from the sensor to the bottom plane of the coil is 6mm (The smaller, the better. 6mm is the minimum value that we can set because of the big size of the circuit board of the sensor). To simulate the insulator outside the pipes, firstly 2mm lift-off was applied. Concerning this mode, there are mainly two aspects of advantage: (1) FG sensor only measures the signal of the perturbed field that is affected by the existence of defect because the direct magnetic field of vertical direction (generated by exciting current in coils) at the position of FG sensor could be counteracted to be zero.

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The perturbed field is rather small, thus the small measurement range of FG sensor can be satisfied. (2) Eddy current in the specimen decreases very slowly along depth direction and deeper penetration depth could be expected.

(a) Differential exciting mode

(b) Exciting coils and FG sensor

Figure 7. Differential exciting mode and coils Table 1. Parameter of exciting coils Items ID OD Height Wire diameter Turn Impedance (at 50Hz) Distance between two coils

Coil 1

Coil 2 30mm 30mm 60mm 60mm 30mm 30mm 1mm 1mm 389 387 1.847Ohm 1.850Ohm 80mm (center to center)

3. Results and discussion 3.1. Results of local wall-thinning detection in one layer pipe In this study, the local wall-thinning on the bottom side of a plate (shown in Figure 3, 20mm thick) is to be detected using the above pulsed ECT system and FG sensor. The magnitude of the DC part of the pulse exciting current is 4A for each coil, the period is 0.02s, duty is 50%. The pick-up signal collected by the FG sensor was averaged over 100 cycles of the transient output for duration of 2.0s, to reduce noise. Inspection condition is shown in Figure 8. In experiments, scanning signals were obtained using scanning stage and the center of the defect was chosen as the origin. The center of two exciting coils (also the position of FG sensor locates at) started from the point which is 75mm far from the origin point (coordinate is -75mm) and moved along the scanning direction to the position of 75mm coordinate in which the interval of every step is 3mm. The peak value at every scanning point was extracted from the pick-up signal to detect the slot defect of the plate. Figure 9(a) shows the results of three specimens with different size of slot defect. Figure 9(b) shows the relationship between “value of peak to peak” of scanning signal and the size of defect. We can see that local wall-thinning in one thick layer could be detected and different size of defect has different “value of peak to peak”. This lays a good foundation for the future quantitative work.

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Figure 8. Inspection condition

(a) Scanning signal (b) Relationship between “value of peak to peak” of scanning signal and size of defect Figure 9. Pick-up signal and relationship between signal and defect

3.2. Results of local wall-thinning detection in double layer pipes In this study, the local wall-thinning on the bottom side of the lower layer in double layer plates (shown in Figure 4, 8mm plus 8mm thick) is to be detected using the same experiment system and the same parameters of exciting signal as in section 3.1. Inspection condition is shown in Figure 10. In experiments, S1 is the pick-up signal at position 1 where sensors are far from defect (ideally S1 is 0) as the reference signal. S2 is the pick-up signal at position 2 where the center of coil 2 locates at the center of the defect.

Figure 10. Inspection condition

Figure 11(a) shows the results of differential signal (S2-S1) of the three specimens with different depths of slot defect using FG sensor and Hall sensor, respectively. The results show that FG sensor is much better than Hall sensor for small defect detection in a thicker specimen because of the big noise level of Hall device. Similarly Figure 11(b) shows the relationship between pick value of the differential signal and the depth of the defect. We can see that local wall-thinning in double layer pipes could be detected and different depth of defect has different peak value. This also lays a good foundation for the future quantitative work.

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(a) Pick-up signal using FG sensor and Hall sensor

(b) Relationship between peak value and depth of defect

Figure 11. Pick up signal and relationship between signal and defect

4. Conclusion In the paper, it has been analyzed how to choose a suitable duty of square wave pulse in pulsed ECT method. A differential exciting mode was developed to efficiently apply TMF-FG sensor in pulsed ECT experiment system. The experiment results state that local wall-thinning in one thick layer pipe (20mm) and double layer pipes (8mm+8mm) with small lift-off (2mm) could be detected using the above detection mode. In addition, experiment result shows that FG sensor is much better than Hall sensor for small defect detection in thicker specimen. This study gives a good foundation for the future quantitative work. Acknowledgements This work was conducted as a part of Nuclear and Industrial Safety Agency (NISA) project on Enhancement of Ageing Management and Maintenance of Nuclear Power Plants in Japan and supported by the Grant-in-Aid for the Global COE Program, "World Centre of Education and Research for Trans-Disciplinary Flow Dynamics", from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. The authors would like to thank Mr. Takeshi Sato of Tohoku University, for the preparation of the specimens and the fabrication of the probe. References [1] G.Y. Tian, A. Sophian. Defect classification using a new feature for pulsed eddy current sensors. NDT&E International 38 (2005) 77-82. [2] J. Kim, G. Yang, L. Udpa, S. Udpa. Classification of pulsed eddy current GMR data on aircraft structures. NDT&E International 43 (2010) 141-144. [3] M. Fan et al. Analytical modeling for transient probe response in pulsed eddy current testing. NDT&E International 42 (2009) 376 383. [4] T. Chen et al. Feature extraction and selection for defect classification of pulsed eddy current NDT. NDT&E International 41 (2008) 467 476. [5] M. Morozov, G.Y. Tian and D. Edgar. Comparison of PEC and SFEC NDE Techniques. NDT&E International 24 (2009) 153 164. [6] G.Y. Tian and A. Sophian. Study of magnetic sensors for pulsed eddy current techniques. Insight 47 (2005) 277-279. [7] M. Valentino, G. Pepe, A. Ruosi and G. Peluso. Eddy-current nondestructive measurements with different HTS-SQUID spatial orientations. J. Phys. IV France 8 (1998) 249-252.

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Developing ECT System with AMR Sensor for Combustion Chamber Dongfeng HE a,1, Mitsuhara SHIWAa, Jianping JIAa, Hisashi YAMAWAKIa, Ichizo UETAKEa, Junji Takatsubo b, Shinichi MORIYAc, and Koichi OKITAc a National Institute for Materials Science, Sengen 1-2-1, Tsukuba, 305-0047, Japan b Advanced Industrial Science and Technology1-2-1 Namiki, Tsukuba, 305-8564, Japan c Japan Aerospace Exploration Agency, Sengen 2-1-1, Tsukuba, 305-8505, Japan

Abstract. An eddy current testing (ECT) system with a high sensitive AMR sensor was developed. In our experiments, a specimen of cooper plate with grooves and slits was used to simulate the cooling grooves of the combustion chamber of liquid rocket and the defect in it. Three defects, with the width of 0.2 mm, the length of 4 mm and the depth of 0.2 mm, 0.5 mm and 0.8 mm respectively, were made in the bottom of the grooves. Using a Φ 4.5 mm and 30 turn circular excitation coil, ECT experiments were done for the AMR sensor with Z, X and Y directions at the frequency of 2 kHz. The results show that the variance of lift off had big influence on the ECT result with the Z direction AMR sensor and smaller influence on that with the X, Y direction AMR sensor. The defects with the depth of 0.8 mm and 0.5mm, 0.2 mm were clearly observed, but the signal of the defect with the depth of 0.2 mm was very small. Keywords. ECT, AMR, combustion chamber

Introduction For the liquid rocket, liquid Oxygen and liquid Hydrogen are used as the propellant. The wall of the combustion chamber is made of Cu-Cr-Zr copper alloy. High temperature gas over 3000 K is generated in the combustion chamber and liquid hydrogen flowing in the cooling groove is used for the cooling. Due to the big thermal gradient and the excessive thermal strain generated in the cooling groove, two kinds of damages might be generated in the wall of the combustion chamber. One is from the inner wall side, which is caused by the oxidation/reduction of the oxide layer; another is the melt damage from the cooling grooves, which is caused by the growth of the small crack in the grain boundary of the copper alloy. The aim of this research is to find an effective method for the tiny defect detection and evaluation of the combustion chamber. Eddy current testing (ECT) is an effective method to detect defects in conductive materials. It has the advantage of low price and easy operation. Inductive coil, anisotropic magneto resistance (AMR), giant magneto resistance (GMR), flux gate, superconducting quantum interference device (SQUID) have been used as the sensors in ECT systems [1-4]. SQUID has the best magnetic field resolution especially at low frequency. However, SQUID must be cooled by liquid nitrogen or liquid helium, so the ECT system with SQUID is expensive, complex and is not easy to handle. High sensitive flux gate is also expensive. The sensitivity of coil become worse at low

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frequency and GMR sensor also has big noise at low frequency. AMR sensor is cheaper than SQUID and flux gate and has better sensitivity than inductive coil and GMR sensor at low frequency. Using the low noise driving circuit developed by us, the magnetic field resolution of AMR sensor was improved to 12 pT/√Hz at the frequency of above 1 kHz [5]. The driving circuit operated in amplifier mode or feedback mode and the linearity could be improved for feedback mode, which is important for a moving ECT system in unshielded environment. ECT experiments were once been done for an aluminum plate [6]. In this report, we will present our ECT results for the specimen of copper plate with the X, Y, and Z sensing directions of the AMR sensor.

1. Experimental setup Figure1 shows the block diagram of the ECT system with AMR sensor. The circular coil was used to produce the excitation field. Then, eddy-current was induced in the specimen. If there was some defect in the specimen, the distribution of the eddy-current was changed and the field produced by the eddy current was detected by the AMR sensor. Through the lock-in amplifier, the amplitude signal and the phase signal could be obtained; then it was sent to a computer for data acquisition and data processing. In our experiment only the amplitude signal was used. The AMR sensor was fixed with the X-Y stage for the scanning.

Figure 1. The block diagram of the ECT system with AMR sensor

1.1. Specimen To simulate the real combustion chamber of liquid rocket, the specimen was made of copper alloy plate. Figure 2 shows it. The thickness of the plate was 4 mm. Grooves with the width of 1 mm and the depth of 3 mm were made on one side of the copper plate. Three slit defects were made in the bottom of some grooves with the length of 4 mm, the width of 0.2 mm and the depth of 0.2 mm, 0.5 mm, and 0.8 mm respectively. The surface of the copper was not flat; bending exists in some part of the copper plate, which caused the variance of the lift off.

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Figure 2. The specimen of copper plate with grooves and slit defect to simulate the combustion chamber of liquid rocket.

1.2. AMR sensor and the driving circuit A commercially available AMR sensor of HMC1001 was used [7]. The magnetic field sensitivity of the AMR sensor was about 3.2 mV/V/Gauss. To improve the field resolution, higher bias voltage of 24 V and low noise preamplifier were used. To improve the linearity of the response, a driving circuit operating in feedback mode was designed [5]. The AMR sensor has flat response till to 5 MHz and the magnetic field resolution was about 12 pT/√Hz at the frequencies of above 1 kHz. 1.3. The excitation coil and the sensing direction of AMR sensor A 30 turn, Φ 4.5 mm circular coil was used to produce the excitation field. Figure 3 shows the three sensing direction of the AMR sensor. Figure 3 (a) shows the Z direction AMR sensor. The coil was attached to the bottom of the AMR and the position was adjusted to get the biggest output for the excitation field. Figure 3 (b) shows the X direction sensor. The sensing direction of the AMR sensor was along the direction of the groove. The coil was attached to one side of the AMR sensor and the position of the coil was adjusted to get the smallest output. Figure 3 (c) shows the Y direction sensor. The sensing direction of the AMR sensor was perpendicular to the groove’s direction.



D  D 

E E 

F F 

Figure 3. The excitation coil and the sensing direction of AMR. (a). Z direction. (b). X direction. (c). Y direction

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1.4. The experimental condition The conductivity of the copper alloy is about 5.8™106 S/m. In our experiments, the excitation frequency was 2 kHz. From the formula δ

= 1 πfμσ , where, δ is the

penetration depth, f is the excitation frequency, μ is the permeability of the material and σ is the conductivitythe penetration depth is about 1.5 mm for copper alloy at 2 kHz. The amplitude of the current flow in the excitation coil was about 20 mA. The amplitude of the magnetic field at the center of the coil was about ±2 Gauss. X direction was parallel to the direction of the grooves, Y direction was perpendicular to the direction of the grooves, and Z direction was vertical direction perpendicular to the surface of the specimen. For the XY scanning, first, fixing the X position and line scanning along Y direction; then changing the X position. Due to the bending of the specimen, the variance of the lift off was from 0.2 mm to 1mm.

2. Experimental results We did the ECT experiments for the AMR sensor with Z direction, X direction and Y direction. For the Z direction sensor, the big excitation field was also detected by the AMR senor. For the X and Y direction sensor, the excitation field was not detected by the AMR sensor. 2.1. Z direction Figure 4 shows ECT results when using the AMR sensor with Z direction. Figure 4 (a) shows the Line scanning where the defects exist. Figure 4 (b) shows line scanning where no defects exist. Figure 4 (c) shows the 2D contour map of the XY scanning results. The defects with the depth of 0.8 mm and 0.5 mm were observed. Due to the big background field and the influence of the variance of the lift off, the smallest defect with the depth of 0.2 mm was not observed.

Figure 4. ECT results using AMR with Z direction. (a). Line scanning result where defects exist. (b). Line scanning result where no defects exist. (c). Contour map of the XY scanning results.

Figure 5 (a) shows the subtraction results of the line scanning Figure 4 (a) and Figure 4 (b). Figure 5 (b) shows the 2D contour map of the subtraction results. The

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defects of 0.8 mm and 0.5 mm become clearer; A very small signal appeared for the defect signal with the depth of 0.2 mm.

Figure 5. (a). The subtraction result of Figure 4 (a) and Figure 4 (b). (b). The contour map of subtraction results.

2.2. X direction Figure 6 shows ECT results when using the AMR sensor with X direction. Figure 6 (a) shows the Line scanning where the defects exist. The defect signal was positive at one end of the defect, and it is negative at another end of the defect. Figure 6 (b) shows the 2D contour map of the XY scanning results. Using the AMR sensor with the X direction, the influence of the variance of the lift off was reduced. A small signal appeared for the defect with the depth of 0.2 mm.

Figure 6. ECT results using AMR with X direction. (a). Line scanning result where defects exist. (b). 2D Contour map of the XY scanning results.

2.3. Y direction ECT experiments using AMR sensor with Y direction were also done. Figure 7 (a) shows line scanning results where defects exist. For each defect, a peak and a valley signal appeared. The defects with the depth of 0.8 mm and 0.5 mm were clearly

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observed. The signal of the defect with the depth of 0.2 mm was small. The influence of the variance of lift off was also reduced. Figure 7 (b) shows the contour map of the results.

Figure 7. ECT results using AMR with Y direction. (a). Line scanning result where defects exist. (b). 2D Contour map of the XY scanning results.

3. Summary ECT system with AMR sensor was constructed and ECT experiments for the copper specimen were done using the AMR sensor with the Z, X and Y directions. Variance of lift off had big influence when using Z direction AMR sensor. The influence of the variance of lift off was reduced when using X and Y direction AMR sensor. The defects with the depth of 0.8 mm and 0.5 mm were observed. The signal of the defect with the depth of 0.2 mm was very small.

Acknowledgment We thank the helps from Prof. H. Itozaki and Dr. M. Tachiki.

References [1] K. Allweins, M. von Kreutzbruck, G. Gierelt, “Defect detection in aluminum laser welds using an anisotropic magnetoresistive sensor array”, J. Appl. Phys., 97, 10Q102, (2005) [2] T. Dogaru, S.T. Smith, “Giant magnetoresistance based eddy current sensor”, IEEE Trans. Magn., 37, pp.2790 2793, (2001). [3] C. Carr, J.C. Macfarlane, “The performance of flux gate magnetometers for nondestructive evaluation”, Insight, 41, pp.20 24, (1999). [4] H. Weinstock, R.A. Welsh, “SQUIDs for nondestructive evaluation, Superconductor Industry”, 10, pp.23 28, (1997). [5] D.F. He, M. Tachiki, H. Itozaki, “Highly sensitive anisotropic magnetoresistance magnetometer for Eddy current nondestructive evaluation”, Rev. Sci. Instru , 80, 036102, (2009). [6] Dongfeng He, Mitsuharu Shiwa, et al., “Basic Examination for the Defect Detection of Combustion Chamber Using ECT”, submitted to Journal of JSNDI, (2010).

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Flux Leakage Measurements for Defect Characterization Using NDT Adapted GMR Sensors Matthias PELKNER1, Andreas NEUBAUER, Mark BLOME, Verena REIMUND, Hans-Martin THOMAS and Marc KREUTZBRUCK Federal Institute for Material Research and Testing Unter der Eichen 87, D 12205 Berlin, Germany

Abstract. High precision magnetic field sensors are of increasing interest in non destructive testing (NDT). In particular GMR sensors (giant magneto resistance) are qualified because of their high sensitivity, high signal to noise ratio and high spatial resolution. We performed magnetic flux leakage measurements of artificial cracks with a GMR gradiometer and a 3 axes GMR magnetometer. Cracks of a depth of 44 μm still could be detected with a sufficient high signal to noise ratio. A semi analytic magnetic dipole model was used for swiftly predicting magnetic stray fields. The reliable reconstruction based on measurements of artificial rectangular shaped defects is demonstrated. Keywords. GMR, NDT, magnetic flux leakage, reconstruction

Introduction Magnetic flux leakage testing (MFL) is one of the most popular methods for defect detection and characterization of magnetic components in NDT. The most prominent method for a MFL application is the magnetic particle inspection (MP). In this method magnetic particles accumulate at magnetic stray fields generated by surface cracks in a magnetized component. By means of MP the number of defects and their length can be determined precisely. However, the estimation of defect depth and the automation of MP-applications is rather difficult. To examine the depth and width of inhomogeneities in more detail it is necessary to measure the stray field near cracks. This can be done by any magnetic field sensor, such as flux gate sensors, hall probes, SQUID, or XMR sensors (magneto resistance; X = G (giant), A (anisotropic), etc.) [1-6]. In this work we used two types of GMR (giant magneto resistance) sensors optimized for NDT applications: a gradiometer measuring the normal component of the magnetic flux leakage and a new 3-axes magnetometer measuring all three directions in space. GMR sensors are well suited for NDT applications thanks to their high sensitivity, high signal-to-noise ratio and small sensing area associated with a high spatial resolution. In contrast to commercial GMR sensors that are usually embedded in a bulky encapsulation, the sensitive layers of the GMR sensors used in this work are located 1

Corresponding Author: E mail: [email protected]. This work is supported by the Federal Ministry of Education and Research, Germany, project no. 16SV3787.

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only a few tens of μm from the chip edge, resulting in a small sensor-to-surface distance. This helps to visualize the defect signature with a very good spatial resolution. Further, having a fast inverse scheme in mind based on a semi-analytic model for MFL to estimate the defect parameters like width, depth and length, it is helpful to work with “point-like” sensing devices. Therefore the active sensing area should be adapted to the liftoff and has to be smaller. Otherwise, the field gradients along the active area must be considered via integration over the whole sensing area, leading to distinct layers calculation times.

1. GMR sensors and semi-analytical model for MFL. 1.1. Experimental setup The experimental setup consists of three high precision manipulators (Aerotech) for the three directions in space, providing a maximum scanning velocity of 0.5 m/s and a spatial resolution of 1 μm. The manipulators are fixed on a 2000 kg bloc of granite eliminating environmental vibrations. To record the data of the sensors a fast data acquisition hardware based on a 18 bit AD-converter with a maximum sampling rate of 600 kHz (National Instruments) was used. To achieve a high signal-to-noise ratio, the sensor signals were pre-amplified. 1.2. GMR gradiometer and 3D magnetometer

(a)

(b)

Figure 1. GMR gradiometer measuring the gradient in x direction of the normal field component Hz. (a) Sketch of the electric circuit of the GMR chip (Sensitec GmbH). The sensing areas (R1 R4, green and red) are sensitive to Hz. The distance between R2/R4 and R1/R3 is 250 μm. (b) Schematic of an artificial crack with dimensions length l, depth h and width w. The induced polarization on the defect wall is indicated by plus signs. The white squares represent the sensing elements of the GMR gradiometer above the defect.

The GMR effect was discovered in 1988 by Peter Grünberg [7] and Albert Fert (Nobel Prize in Physics, 2007). Independently they found a “giant” magneto resistance (GMR) in a multilayer structure consisting of ferromagnetic layers divided by nonmagnetic

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layers which depend on the directions of magnetization in each layer. The effect is based on quantum-mechanical scattering of the conduction electrons at the boundary surface between the ferromagnetic and nonmagnetic layer. Generally a GMR gradiometer consists of four not-shielded elements fabricated as a Wheatstone-bridge as shown in fig. 1(a), resulting in a distinct temperatureindependent output signal. The measured quantity is the difference of the magnetic field (here the normal component Hz) between the two active areas and it is detected by measuring the bridge voltage. In our case, the sensing areas have a size of only 70×60 μm² and a transfer function of 14 mV/V·(kA/m)-1 in its linear range between ± 1kA/m. The 3-axes magnetometer (Sensitec GmbH) consists of three Wheatstone bridges that allow to measure absolute field values via special flux concentrators. As its prominent feature the new 3-axes magnetometer detects simultaneously all three spatial components of the magnetic field in the same parallel plane next to the surface under investigation. Fig. 2 depicts the layout of the sensor. The x and y components are measured with special flux concentration layers, which are rotated by 90°. Both flux concentrators have a diameter of 140 μm. This results in a spatial resolution that is worse than for the gradiometer described above. The z-component is measured by the field distortion in the vicinity of two flux concentrator strips with dimension about 10×160 μm² and separated by a distance of 30 μm. The transfer function for the 3-axes magnetometer is 30 mV/V· (kA/m)-1 and it has its linear range for fields between ± 1kA/m. For further details see [8].

Figure 2. Prototype of a 3 axes GMR magnetometer (Sensitec GmbH) measuring the three directions in space of the magnetic field in the same plane. On the right a SEM picture of the 3 axes magnetometer is shown [8].

1.3. Semi analytic model Inversion of MFL signals requires an adequate forward solver for predicting magnetic stray field signals. To account for defects we employed the magnetic dipole model intro-duced by Shcherbinin [9,10]. According to this model MFL signals arise due to induced magnetic polarizations on the defect walls [11]. This model allows to calculate magnetic stray fields of a rectangular defect with length l, width w and depth h (see fig. 1(b)). Especially for GMR sensors that can be positioned very close to the surface of the test piece, it is important to carefully consider the dimensions of the probe, i.e., the size of their active sensing areas, in the calculation process. In our calculation we therefore numerically integrated the magnetic stray field expressions over the active sensor areas of the GMR testing probe (fig. 1(b)) to obtain a fast algorithm.

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For the inverse calculation of the defect parameters we employed the trustt-region reflective algorithm to minimize the difference between the predicted( dsyn F(m) ) and measured ( dobs ) GMR sensor data iteratively using an L2 norm approach. Initially, the forward solution is estimated for an arbitrarily chosen start model m0 (comprising the defect parameters l, w and h). Subsequently, the sought-after model parameters are updated in an iterative fashion by minimizing the objective function

dobs

2

j j dsyn with dsyn

F(m j )

,

(1)

where j denotes the iteration number and F(m j ) the forward solution step as outlined above. Minimization is continued until convergence is reached yielding an estimate of the true defect parameters.

2. Results As test object we used a steel plate with artificial cracks of varying depth (see fig. 3). The artificial cracks were introduced by electrical discharge machining. The width of the cracks varies between 100 to 200 μm with a length around 5500 μm. The depth ranges between 10 μm and 2240 μm. The measurements were performed in remanence (no applied field during measurement), i.e., the test object was magnetized before. The direction of the applied field was normal to the defect geometry.

Figure 3. Schematic cross section of the steel plate. The field was applied along the x direction.

2.1. Gradiometer detecting the z component of the magnetic field Using the gradiometer line scans with different liftoffs were recorded. Fig. 4 shows the gradient of the magnetic stray field as a function of position x. Clear signatures of the field gradient illustrate the defect positions and the amplitude of ΔH scales with the depth of the defects [11]. The right panel in fig. 4 illustrates the signals of the defects with a depth between 44 μm and 380 μm in more detail. The attenuation of the signal for an increasing liftoff is in agreement with the theoretical model. Further, it is found that even the 44 μm deep defect can be observed. However, for the 30 μm and 10 μm deep cracks no clear signal can be distinguished from the noise. Possible contributions to the noise level may originate from the roughness of the surface or from spatial variations of the permeability.

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Figure 4. Line scan with a gradiometer for three different distances between sensor and surface of the test object.

2.2. Reconstruction Magnetic field sources generally create a blurred magnetic field distribution above the sample’s surface. This is due to the divergence of the magnetic field and the position of the sensing device, which in an exterior investigation is naturally always a certain distance from the source of the field. What starts as a distinct field distribution inside the sample turns into a broad field distribution when the field sensor is either too large or positioned at too far a distance above the sample’s surface. This blurredness complicates the data interpretation and begs for additional support through signal processing to evaluate the mechanical state of the sample. Thus, small sensors providing high spatial resolution in combination with a large signal-to-noise ratio are helpful to gain better insight into the type of defect, its size and its location. In fig. 5 the measurement and the results of the reconstruction of two defects are shown. For the reconstruction data in the vicinity of the defect was used to calculate the defect parameters (approx. 120,000 data points). The false rendering plots in the upper panel of fig. 5(a) show the experimental and calculated data of the stray field gradient of a 210 μm deep crack. In addition 10 line scans across the defect, extracted from both data sets, are shown aside. In the lower panel of fig. 5(a) the results of the reconstruction process are shown, in which the parameters length, depth and width were reconstructed simultaneously. A relative fast converging process is observed. The length converges after less then 10 iterations and the depth can be reconstructed after less than 5 iterations. In total this reconstruction requires only a few seconds on a standard PC. It is worth mentioning that the crack width does not converge to the real value. This is in agreement with the sensitivity matrix and is due to the fact that in the analytical model the crack width has a minor influence to the stray field [11]. Remarkably, we find a good reconstruction quality also for the 44 μm-deep defect although dealing with a significant decrease in SNR, as illustrated in fig. 5(b).

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Figure 5. False color renderings of two different defects: (a) 210 μm and (b) 44 μm deep. The top left picture shows the measurement and the middle one the synthetic generated signal form of the reconstruction algorithm. Right to them ten lines are exemplary illustrated ( measurement, simulation). In the bottom diagram the defect parameters and the steps of reconstruction are presented.

2.3. 3 axes Magnetometer Finally, in this section first measurements of the magnetic flux leakage using a new 3axes magnetometer are shown. The same test plate was used as for the gradiometer. The prototype 3-axes magnetometer measures Hx, Hy and Hz simultaneously at the same lift off. This provides additional information of the magnetic field which is required, e.g., for a more voxel-based reconstruction algorithm. In fig. 6 the results for the Hx and Hz component of the magnetic field are presented. Panel (a) and (c) show false rendering plots for both magnetic field components. For each field component three line scans, indicated by the black, red and green line, are shown in panels (b) and (d). These line scans illustrate the stray field at the edges (black, green) and the center (red) of the cracks, respectively. As expected from the analytic model, the stray field signals are most pronounced in the center of a crack and decline towards the edges. Since a magnetometer was used the defect signals appear superimposed on magnetic stray fields originating from the magnetic steel plate itself. The typical signatures of these background fields are a maximum in the center of the plate for the Hx component and a gradual decline for the Hz component. The Hy field component (not shown) is characterized by MFL signatures at the edges of the long sides of the cracks. Since the direction of the magnetization was along the x direction, only at these end positions distinct signatures of Hy are expected.

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Figure 6. Stray field distribution represented in a false color renderings. (a) False rendering plot of field component Hx. (c) Hz component. (b) and (d): Extraction of 3 line scans across the left and right edge of the crack (black and green) and the center of the crack (red), where field amplitude is maximum.

In fig. 7 the scanning area was adapted to three defects for the Hx component of the magnetic field. Compared to the gradiometer we observe a somewhat higher noise level. In addition to the 380 and 210 μm deep defects the 44 μm deep defect can be imagined.

Figure 7. Field distribution of the Hx component measured by a 3D magnetometer. Extraction of defects with a depth of 380, 210 and 44 μm.

3. Conclusion The automation of flux leakage testing is an active research field, where the use of adapted magnetic field sensors detect stray field distributions of defects above the test specimen. For this purpose, the sensors require a high spatial resolution and an excellent field sensitivity. We therefore propose in this work the use of NDT-adapted GMR sensors that enable us to detect several artificial defects with depth down to 44

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μm. Detecting the magnetic field close to the surface offers the advantage to obtain more detailed information on the geometrical parameters of the defects. Using a few μm-sized GMR gradiometer, where the sensing MR-layer is positioned close to the chip edge, we obtained distinct crack signatures with good spatial resolution and showed that a reconstruction of the length and depth can be reliably carried out. The width can also be determined, however, less accurate due to the smaller influence of the width on the stray field. In addition we proposed the use of a 3-axes magnetometer measuring all three field component simultaneously. These results can be regarded as a further step towards the use of GMR sensors in NDT providing a more complete picture of the real magnetic field distribution of the sample’s outside world. This paves the way for new visualization techniques, precisely defect localization, defect characterization, and tomography-like mapping techniques. Electromagnetic testing based on small magneto resistive layers with high spatial resolution can be provided with relatively high cost effectiveness. This also allows GMR-sensors to follow the miniaturization trend providing an adequate testing method for quality control of small components. GMR-technology thus has the potential to bridge the micro-gap between the mm-sized conventional induction coils for detecting macroscopic material defects and the scanning magnetic force microscopy for the detection of field distribution on the nm-scale.

References [1] K. Allweins, M. v. Kreutzbruck, G. Gierelt, Defect Detection in Aluminium Laser Welds Using an AMR Sensor Array, J.Appl.Phys. 97 (2005), 10Q102 [2] H. Pries, Giant Magnetic Resistance Sensoren in der industriellen ZfP, Report of Annual Meeting of the German Society of Nondestructive Testing 2008, St. Gallen, Switzerland [3] Y. Kataoka et al., Application of GMR line sensor to detect the magnetic flux distribution for nondestructive testing, International Journal of Applied Electromagnetics and Mechanics 15 (2001/2002), 47 52 [4] H. J. Krause, M. v. Kreutzbruck, Recent Development in SQUID NDE, Physica C 368 (2002), 70 79 [5] C. Dolabdjian, G. Waché, L. Perez, Improvement in the detection of subsurface fatigue cracks under airframe fasteners using improved rotating giant magneto resistance magnetometer head, Paper presented at the 9th European Conference on NDT, 25 29 September 2006, Berlin [6] F. Gruhl, M. Mück, M. v. Kreutzbruck, J. Dechert, A scanning superconducting quantum interference device microscope with high spatial resolution for room temperature samples, Rev. Sci. Instrum. 72 (2001), 2090 2096 [7] P. Grünberg, et al., Layered Magnetic Structures: Evidence for Antiferromagnetic Coupling of Fe Layers across Cr Interlayers, Phys.Rev.Lett. 57 (1986), 2442 [8] C. Glenske, U.Loreit, New 3D Magnetic Field Sensors with GMR Spin Valve Layers, Paper presented at the 10th Symposium Magnetoresistive Sensors and Magnetic Systems, 31. March/1. April 2009, Wetzlar (Germany) [9] N. Zatsepin, V Shcherbinin, Calculation of the magneto static field of surface defects. I. Field topography of defect models, Defektoskopija 5 (1966), 50 59 [10] V. Shcherbinin, A. Pashagin, Influence of the extension of a defect on the magnitude its magnetic field, Defektoskopija 8 (1972), 74 83 [11] F. Förster, New findings in the field of non destructive magnetic leakage field, NDT International 19 (1986), 3 14

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-225

225

Evaluation of EMAT signals using magnetostrictives for imaging a

Yoshihiro NISHIMURA a,1 , Akira SASAMOTO a and Takayuki SUZUKI a National Institute of Advanced Industrial Science and Technology, 1-2-1 Tsukuba Ibaraki-prefecture, 305-8564, Japan Abstract. Electromagnetic acoustic transducers (EMATs) is a means of contact free nondestructive testing (NDT). They are useful for high speed scanning of in spection materials or for scanning high temperature materials. EMATs have inter nal permanent magnets that induce a strong magnetic field in the inspected mate rials. They employ pulsing current to induce eddy currents on the surface of in spected materials and generates an ultrasound signal by Lorenz force or by magne tostrictive effect in the inspected material. The ultrasound signals propagate to and are reflected from the edge of the inspected material or flaws. The EMAT probe then acquires a time series of echo signals as the output, similar to those derived by piezoelectric transducers. However, the time series of data derived by the EMAT probe is too noisy due to the Barkhausen effect to identify reflections from internal flows, unlike the time series of data derived by the piezoelectric probe. We em ployed a low pass filter method and Z direction averaging method to decrease the Bartkhausen noise and compared them. Keywords. EMAT, image reconstruction, Hilbert transformation, Barkhausen noise

Introduction In these years, technology for imaging flaws in structural materials using non-destructive testing methods has become important for the safety of society. The recent progress of high speed computational ability of PCs has enabled the widespread use of flaws imaging technology.[1][2][3] Conventionally, piezoelectric probes have been employed for detecting and imaging flaws in structural materials. Piezoelectric probes usually are in contact with samples directly or are indirectly coupled through water and therefore cannot easily scan samples quickly. Piezoelectric probes are not available for detecting flaws in large samples. An electromagnetic acoustic transducer (EMAT) is a major nondestructive (NDT) device that detects flaws in a sample using an ultrasound signal induced by electromagnetic force.[4] EMAT can address the problem of slow-speed scanning because EMATs can scan without contacting the samples. An EMAT measures a time series of data, that is waveforms similar to those produced by ordinary piezoelectric transducers. Two kinds of EMAT are availables, one using Lorenz force and another using magnetostrictive ef1 Corresponding Author: Yoshihiro Nishimura, AIST, 1 2 1 Namiki Tsukuba Ibaraki, Japan; E mail: [email protected].

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fects. The latter can be used for easily detecting flaws in a sample with ferromagnetic oxide scale. However, the data generated by EMAT using magnetostrictive effects are very noisy due to the Barkhausen effect, compared to data produced by ordinary piezoelectric transducers. It is important to decrease such noise to reconstruct images of flaws in samples because the noise from Barkhausen effects is sometimes too large to ignore. Of course, some noises come from electoronic amplifier circuit also. Such noise can be decreased by staying at one position and averaging over a time series of data derived repeatedly. However, if the probe scans a large surface area on a sample in a limited time for imaging , the probe cannot remain long at one position for averaging. The frequency of these noise is much higher than that of the significant signal data. A low-pass filter, that can remove high frequency noise, is one way to address this problem but introduce another kind of noise. Some other method for reducing noise when imaging flaws should be explored. 1. EMAT Principles An EMAT is used in an NDT method similar to the conventional ultrasound testing (UT), except that its probe output signal has more noise and that it is a contact-free method. The EMAT probe has a coil (or coils) and a strong internal magnet (Figure.1). Pulsing

Figure 1. EMAT operation principles

current induces eddy current on the surface of the inspected material as much as the eddy current testing (ECT) probe does. The induced eddy current generates an ultrasound signal by Lorenz force or by magnetostrictive effect( Figure.1). The ultrasound signal propagates to and reflects from the edges of the sample or the flaws (Figure.2). The probe output is observed as a time series of echo signal intensities on the EMAT screen( Figure.3). A typical time series of data derived by an EMAT from reference specimen is depicted in Figure.3. The initial peak induced by the first current pulse and many subsequent peaks from multiple reflections at the edge of reference sample can be observed. The initial peak is too large compared to later peaks and so is saturated in the full input scale range. This measurement was made at 2GHz.

Y. Nishimura et al. / Evaluation of EMAT Signals Using Magnetostrictives for Imaging

227

Figure 2. Signal propagation in EMAT operation

Figure 3. EMAT signal observed from reference specimen sample at 2GHz

2. EMAT Signals From Sample With Oxide Scale Surface A sample with some internal flaws was prepared. Its geometry and dimensions are depicted in Figure.4. Its oxide scale was generated in an environment similar to those of actual use. The 3-D scanner depicted in Figure.5 was developed and applied to the prepared sample. A FA computer controlled the scanning movement of the EMAT probe and the trigger timing of the pulser/receiver. An AD converter collected the time series of data from the receiver and the FA computer stored them in its data strorage. A block diagram of the 3D-scanner is presented in Figure.6. Scanning was done as illustrated in Figure.7. The specification of the 3D scanner are listed in Table.1. The measurement was made under the configuration listed in Table 2. The observed time series of data is very noisy, as illustrated in Figure. 8(a),(b), but averaging measured data(time-based-averaging) can decrease such noise (Figure.9(a),(b)). These noisy signals were observed all over the surface and can be decreased by averaging.

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Figure 4. Sample’s geometry and dimensions

Figure 5. 3D scanner Table 1. 3D Scanner Specifications. Scan speed

1 line/s(max 1000m/s)

Precision(X,Y,Z)

0.5μ m

Maximum image resolution

8192× 8192

Measurable area

360mm× 310mm× 80mm

Table 2. Scanning condition. Scan area

75mm× 75mm

X Y resolution

1024x1024

Sampling rate

400MHz

Sampled Number

16000

If the probe scans a large surface area on a sample in a limited time, the probe cannot stay long at one position for averaging. The time-based-averaging method thus cannot be

Y. Nishimura et al. / Evaluation of EMAT Signals Using Magnetostrictives for Imaging

229

Figure 6. Block diagram of 3D scanning system

Figure 7. The movement of the probe’s scanning over a sample

Figure 8. (a)Raw signal derived from the sample in Figure.4 and (b) Magnified image of reflection signal from bottom edge.

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Y. Nishimura et al. / Evaluation of EMAT Signals Using Magnetostrictives for Imaging

Figure 9. (a)Signal averaged over 400 raw signals derived from the sample(in Figure.4) and (b)Magnified image of reflection signal in (a)

used for scanning a large area. The power spectra of Figures.8(a) and 9(a) are plotted in Figures.10(a) and (b). Most of the noise can be minimized by averaging.

Figure 10. Power spectra of Figure.8(a) and Figure.9(a)

A low-pass filter that passes frequencies below 5.5MHz was applied to the time series data in Figure.8(a). The time series data in Figure.8(a) was converted to the one shown in Figure.11(a),(b). Most of the noise in Figure.8(a),(b) could be removed successfully. However, the low-pass-filtered data reveals noises generated by the filter function at the initial peak in the left half of Figure.11(a).

3. Noise Reduction By Converting 2GHz-sampled Data to 400MHz-sampled Data We tried another noise reduction method. In this measurement, the data was sampled in the X and Y directions at a pitch of 100μm by 3D-scanner. However, the sampling interval in the Z direction is equivalent to a sampling pitch of 7.5μm because the velocity of the transverse wave in steel is 3000m/s and the sampling frequency is 400MHz in

Y. Nishimura et al. / Evaluation of EMAT Signals Using Magnetostrictives for Imaging

231

Figure 11. (a)Signal filtered from Figure.8 by a low pass filter (in Figure.11) and (b)Magnified image of reflection signal in (a)

Figure.8(a). Compared to the sampling pitch in the X and Y directions, the sampling pitch in the Z direction is thought to be too small. We therefore tried 1D-position-based averaging. First, we derived a time series data by sampling at 2GHz. Second, we averaged every 50 samples to derive a time series data equivalent to the one sampled at 40MHz. We tried averaging every 10 samples, every 20 samples , every 50 samples and every 100 samples and decided to employ evey-50-samples-averaging. Sampling the time series data at 40MHz is though to be equivalent to sampling pitch of 75μm in the Z direction. AD converters supporting under 100MHz or 400MHz are used for common uses of UT equipments. AD converters supporting 2GHz or more are not popular. But a 2GHz AD converters was found to be particularly useful for real time noise-reduction and imaging of flaws by such noisy EMAT using magnetostrictive effect.

Figure 12. (a)Signal derived by averaging raw data sampled at 2GHz at every 50 samples raw(in Figure.8) and (b)Magnified image of reflection signal in (a)

In this way, the noise depicted in Figure.8 was decreased successfully. The distributions of reflection intensities in a sample have to be derived to reconstruct a 3D-image of flaws in a sample. By applying Hilbert transformation to the time series data in Fig-

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Y. Nishimura et al. / Evaluation of EMAT Signals Using Magnetostrictives for Imaging

ure.12, a curve illustrating their envelope could be derived in Figure.13(a). Hilbert transformation provides an analytical expression of the signal and its absolute value provides an envelope curve of the signal. A sectional image of the sample can be reconstructed by putting the time T-axis in the vertical direction and the X-axis in the horizontal direction and allocating the the reflection from the flaws at a position (X,T) on the X-T plane. An example of the sectional image of sample is depicted in Figure.13(b). The vertical axis denotes time and the horizontal axis denotes the position in the X direction. The top edge of Figure.13(b) means the surface. The reflection from the flaw and the one from bottom edge can be identified easily and their depth 33mm can be quite precisely measured in Figure.13(b) because the velocity of the transverse wave in steel id 3000m/s.

Figure 13. (a)Envelope curve derived by Hilbert transformation and (b) Reconstructed sectional image of reflected signal

4. Conclusion We investigated the noises of EMAT using magnetostrictives to realize high-speed inspections of large samples. 1D-position-based-averaging method was evaluated by converting 2GHz-sampled signal to low frequency-sampled signal. 1D-position-basedaveraging was found to produce better signal waves in real time. 1D-position-averaging requires the higher performance AD than the one for common use. It maybe a problem for the on-site use.

References [1]

K.Nakahata, S.Hirose, The study of the qualities of the reconstructed image by array probe , JSNDI preceedings, (2006),39 42 [2] R.G.Pratt:Seismic waveform inversion in the frequency domain I Theory and verification in a physical scale model, Geographics (1999), 888 901 [3] Toshiki Watanabe:Full wave inversion, JSNDI Jornal vol 53 (2005), 274 279 [4] Nishimura, Y,. Sasamoto, A,. Suzuki, T,. Study of 3D Image reconstruction using EMAT, Int.J. of Ap plied Electromagnetics and Mechanics, 28(1), p171 176, 2008

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-233

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-241

241

An ECT Probe with Widely Spaced Coils for Local Wall Thinning in Nuclear Power Plants Toshihiro YAMAMOTOa, Tetsuya UCHIMOTOb and Toshiyuki TAKAGIb,1 a Japan Power Engineering and Inspection Corporation b Institute of Fluid Science, Tohoku University

Abstract. Currently, local wall thinning on the inner surface of a pipe is evaluated mostly by ultrasonic thickness measurement from the outer surface of the pipe in nuclear power plants in Japan. However, it has been pointed out that there are two major issues of this evaluation method. Firstly, this method is not able to evaluate local wall thinning from the top of a reinforcing plate that covers the outer surface of a pipe because this two layer structure hinders the propagation of ultrasound. Secondly, because ultrasonic thickness measurement of a pipe wall is conducted at certain intervals on the outer surface of the pipe, it may overlook a hole like defect if the defect size is small compared to this interval. We propose an eddy current testing (ECT) method using widely spaced excitation and pick up coils to alleviate these problems. Our experimental results show this method can be applied to in spection of a double plate that consists of two 8 mm thick austenitic stainless steel plates, and a defect indication is observed in a much larger area than the defect. Keywords. Eddy current testing, Local wall thinning, Pancake coil

1. Introduction In nuclear power plants, local wall thinning on the inner surface of a pipe is evaluated mostly by ultrasonic thickness measurement from the outer surface of the pipe. However, some improvements are still required for thorough and efficient inspection of local wall thinning to maintain aging nuclear power plants. In Japan, it is considered a problem that ultrasonic thickness measurement is not able to evaluate local wall thinning from the top of a reinforcing plate that covers the outer surface of a main pipe around a branch pipe perpendicularly connected to the main pipe because this two-layer structure hinders the propagation of ultrasound (Figure 1). Also, it is of special concern that ultrasonic thickness measurement may overlook a small hole caused by liquid droplet impingement (LDI) because ultrasonic thickness measurement of a pipe wall is conducted at certain intervals on the outer surface of the pipe and the defect size is sometimes smaller than this interval. Decreasing the interval of course reduces the incidence of this problem, but piping maintenance in nuclear power plants already takes an enormous amount of time, and inspection time is not easily allowed to be extended any longer. The aim of this study is to propose an inspection method for two1

Corresponding Author: Professor, Institute of Fluid Science, Tohoku University, 2 1 1 Katahira, Aoba ku, Sendai, Miyagi, Japan; E mail: [email protected]

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T. Yamamoto et al. / An ECT Probe with Widely Spaced Coils for Local Wall Thinning

Figure 1. Reinforcing plate

Figure 2. Absolute probe

Figure 3. Inspection procedure

layer part of piping and to prevent overlooking a hole-like defect on a pipe. The authors have recently reported an eddy current testing (ECT) technique for evaluating local wall thinning [1]. In this technique, an excitation coil and a pick-up coil are aligned at a distance to detect a defect in a deep region after the model of remote field ECT usually used for inspection of small tubes with bobbin coils aligned at a distance [2,3]. Prior to our study, remote field ECT using pancake coils to be applied to flat geometries has been introduced in [4,5], later specialized in inspection of aircrafts. In this study, we assess the applicability of our ECT technique to detection of local wall thinning of a thick-walled double plate and a hole-like defect on a thick-walled single plate.

2. Experiments 2.1. Experimental setup The ECT probe we used in this study has one excitation coil and one pick-up coil shown in Figure 2. The excitation and pick-up coils are 10 mm in outer diameter, 5 mm in inner diameter and 5 mm in height. The number of turns of the excitation and pickup coils is 301 and 3,465 respectively. The wire diameter of the excitation and pick-up coils is 0.2 mm and 0.05 mm respectively. The center-to-center distance between these coils was set to be 50 mm. The equipment used in our experiments consists of a function synthesizer (WF1945B, NF Corporation), a bipolar amplifier (HSA4011, NF Corporation) and a lock-in amplifier (LI5640, NF Corporation). In the experiments, the detection signals were measured while the pair of excitation and pick-up coils was moved on the surface of a plate as shown in Figure 3. The excitation frequency was set to be 1 kHz. 2.2. Specimens Tables 1 and 2 show the information of the specimens used for evaluation of the per-

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Table 1. Rectangular slit specimens Material

316 austenitic stainless steel

Size

500 mm×300 mm×8 mm

Defect

Rectangular slit (Width 10 mm, Depth 1,3,5 mm) Table 2. Square hole specimens

Material

316 austenitic stainless steel

Size

500 mm×300 mm×12 mm

Defect

Square hole (Bottom 10 mm×10 mm, Depth 1,3,5 mm)

Figure 4. Double plate

(a) Plate with a rectangular slit

(b) Plate with a square hole Figure 5. Specimens

formance of our ECT technique. The material of these plates is 316 austenitic stainless steel. A reinforcing plate part of piping was simulated by two 8 mm-thick plates. An intact plate was placed on the top of the other plate that has a rectangular slit on the bottom side as shown in Figure 4. The rectangular slit was cut along a half of the center line on the bottom side in the shorter direction (Figure 5 (a)). A defect caused by LDI was simulated by a square hole. The square hole was made at the center of a 12 mmthick plate (Figure 5 (b)). For each of the rectangular slit and the square hole, three plates were prepared so as to vary the depth of these simulated defects (1 mm, 3 mm and 5 mm). 2.3. Evaluation procedure The specimens described above were inspected from the opposite side of the defect to be detected. Figure 6 shows how we scanned the surface of the specimens. For a double plate with a rectangular slit, five equally-spaced lines along the longer direction of the plate were selected as the scanning lines. Each of the scanning lines has a length of 150

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T. Yamamoto et al. / An ECT Probe with Widely Spaced Coils for Local Wall Thinning

(a) Rectangular slit

(b) Square hole Figure 6. Scanning areas

(a) Original signals

(b) Processed signals Figure 7. Signal processing

(a) Original distribution

(b) Processed distribution

Figure 8. Example of signal processing

mm at 1 mm intervals. The left three lines run above the rectangular slit while the other two do not. For a square hole, a 150 mm×60 mm area at the center of the surface of the plate was scanned. The intervals of scanning were 1 mm in the longer direction and 2 mm in the shorter direction of the plate. 2.4. Signal processing to reduce lift off noise Because the specimens used in this evaluation have a wide-area surface (500 mm×300 mm) and also have a slight warp, the lift-off distance between the probe and the surface

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of the specimens varies with the position of the probe, which causes considerable liftoff noise. To cope with this problem, we processed raw signals obtained from the lockin amplifier. Figure 7 (a) shows the Vx and Vy components of ECT signals obtained from one of the scanning lines going over a rectangular slit in Figure 6 (a). It can be observed that the rectangular slit induces a big change in the signals around the center position. Although the end point of the scanning line is far enough away from the slit, the signal values do not return to zero at the end point. To make the signal values zero at both ends of the scanning line, the voltage value on the line that connects both ends of a signal curve in Figure 7 (a) is subtracted from the voltage value on that signal curve for each point. Figure 7 (b) is obtained in consequence of this processing. For a signal distribution obtained as described in Figure 6 (b), the above processing is applied in the X direction as well as in the Y direction so as to make the values on the boundary of the scanning area zero. Figure 8 shows an example of this signal processing. The removal of gradual changes in the signal distribution highlights a defect indication due to a square hole. 2.5. Results Figure 9 shows the signal distributions obtained from the specimens with a rectangular slit. To simulate a reinforcing plate part, an intact plate was placed on the top of a plate with a rectangular slit as shown in Figure 4. The results indicate that our ECT tech-

(a) 1 mm deep slit

(b) 3 mm deep slit

(c) 5 mm deep slit

Figure 9. Signal amplitude distributions (rectangular slit)

(a) 1 mm deep hole

(b) 3 mm deep hole

(c) 5 mm deep hole

Figure 10. Signal amplitude distributions (square hole)

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T. Yamamoto et al. / An ECT Probe with Widely Spaced Coils for Local Wall Thinning

nique can detect a 1 mm-deep defect on the bottom side of two 8 mm-thick plates. Figure 10 shows the signal distributions obtained from the specimens with a square hole. A 1 mm-deep square hole on the bottom side of a 12 mm-thick plate is clearly recognized in the signal distributions. Defect signals are observed in a much larger area than the defect (The defect area of a square hole is 10 mm×10 mm. The area where a defect indication appears due to a square hole is about 20 mm×40 mm). This property helps prevent overlooking a small defect. Figure 11 shows the relationship between the maximum signal amplitude and the defect depth obtained from Figures 9 and 10. There is an almost linear relationship between them. It implies that the defect depth can be estimated from the maximum amplitude of a defect indication. In above experiments, an LDI defect is simulated by a square hole, but a real LDI defect tends to have a cone shape. Then, a specimen with a cone-shaped hole shown in Figure 12 was also used for evaluation of the detectability of an LDI defect with our ECT technique. The specimen is 300 mm in length, 100 mm in width and 7.1 mm in thickness. The base diameter and the height of the cone-shaped hole are 10.2 mm and 3.6 mm respectively. Because the surface of this specimen is not large enough, the scanning area was reduced from the area described in Figure 6 (b) by decreasing the width in the X direction from 60 mm to 40 mm. Figure 13 (a) shows the signal amplitude distribution obtained by this scanning. The appearance of the defect indication is almost the same as Figure 10, which was obtained with square holes. Figure 13 (b) provides the profiles on the lines X=0 and Y=0 in the amplitude distribution. Whereas the defect is located from -5 mm to 5 mm in both the X and Y directions, a big variation in signal amplitude is still observed at ±10 mm in the X direction and at ±20 mm in the Y direction. This indicates that a defect can be found even if the scanning line is 5 mm away from the edge of the defect with the coils aligned parallel to the scanning line. When the coils are aligned perpendicular to the scanning line, the defect can be found even if the scanning line is 15 mm away from the edge of the defect (Figure 14).

(a) Rectangular slit

(b) Square hole

Figure 11. Relationship between the maximum signal amplitude and the defect depth

Figur 12. Specimen with a cone shaped hole

T. Yamamoto et al. / An ECT Probe with Widely Spaced Coils for Local Wall Thinning

(a) Amplitude distribution

247

(b) Amplitude profiles in the X and Y directions

Figure 13. Signal amplitude distribution (cone shaped hole)

(a) Parallel to the scanning line

(b) Perpendicular to the scanning line

Figure 14. Scanning directions

3. Summary The aim of this study is to propose an inspection method to evaluate local wall thinning on a reinforcing plate part of piping and detect a defect located out of the scanning line. We proposed an ECT technique using widely spaced excitation and pick-up coils to detect a defect on the bottom side of a thick-walled plate. The experimental results show this probe can detect a 1 mm-deep rectangular slit on the bottom side of two 8 mm-thick austenitic stainless steel plates and a 1 mm-deep square hole on the bottom side of a 12 mm-thick austenitic stainless steel plate. There is an almost linear relationship between the maximum signal amplitude and the defect depth. This implies that the defect depth can be estimated from the maximum signal amplitude due to a defect. These defect signals are observed in a much larger area than the defect size. When the coils are aligned perpendicular to the scanning line, this method can detect a defect located within 15 mm from the scanning line. The proposed method can be applied to two-layer structure and detects a defect even if the defect is not on the scanning line. These properties are expected to alleviate concern over ultrasonic thickness measurement conducted for evaluation of local wall thinning of piping in nuclear power plants.

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Acknowledgment This study was conducted as part of Nuclear and Industrial Safety Agency (NISA) project on Enhancement of Ageing Management and Maintenance of Nuclear Power Plants in Japan.

References [1] T. Yamamoto, T. Takagi and T. Uchimoto, Remote field ECT for evaluation of local wall thinning using pancake coils, The 14th International Workshop on Electromagnetic Nondestructive Evaluation (ENDE 2009), 130 132. [2] T. R. Schmidt, The remote field eddy current inspection technique, Materials Evaluation, 42 (2) (1984), 225 230. [3] T. R. Schmidt, History of the remote field eddy current inspection technique, Materials Evaluation, 47 (1) (1989), 14 22. [4] Y.S. Sun, S. Udpa, W. Lord and D. Cooley, A remote field eddy current NDT probe for the inspection of metallic plates, Materials Evaluation, 54 (4) (1996), 510 512. [5] Y.S. Sun, T. Ouang and S. Udpa, Remote field eddy current testing: one of the potential solutions for detecting deeply embedded discontinuities in thick and multiplayer metallic structures, Materials Evaluation, 59 (5) (2000), 632 637.

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-249

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PLL BASED EDDY CURRENT MEASURING SYSTEM FOR INSPECTION OF OUTER FLAW IN TITANIUM ALLOY PLATE Tomasz CHADY1, Jacek KOWALCZYK, Leon NAWOS-WYSOCKI, Grzegorz PSUJ and Ireneusz SPYCHALSKI Department of Electrical and Computer Engineering, West Pomeranian University of Technology, al. Piastow 17, 70-310 Szczecin, Poland

Abstract. In this paper a new nondestructive eddy current system will be presented. The system was design for detection of shallow outer flaws in thick titanium alloy specimens (e.g. plates, discs). A Lock in amplifier was used in a measuring subsystem in order to increase the efficiency of inspections of minor defects. The verification of a performance of the system was done using 6.9 mm titanium plate with artificial EDM (Electrical Discharged Machinated) notches. Keywords. Eddy current testing, measuring system, titanium alloys inspections

Introduction Titanium because of its mechanical properties (high corrosion resistance, high strengthto-weight ratio) is an important material in many leading industries e.g. aerospace. It is commonly used to manufacture new components such as turbine disc. The disc is machined from a titanium billet which is a cylindrical solid bar of up to 400mm of a diameter. In-service failures of such components can often lead to catastrophic consequences with significant economic impact. NDT techniques that are commonly utilized to examine traditional aerospace materials are not always sufficient to detect sub-surface defects created during the manufacturing process in titanium alloys [1]. In the case of components having large diameter a reasonable technique to apply is Ultrasound UT. However its effectiveness is limited to shallow regions close to the component’s surface. This results in a strong need for new advanced NDT technologies for the inspection of titanium components during the manufacturing process. We introduce a novel automated quality control system for the inspection of titanium billets in response to this need in this paper. The system combines two subsystems: eddy current testing (ECT) for evaluation of the material not deeper than 5mm beneath the surface and phased array (PA) ultrasonic for deeper inspection. In this paper the ECT

1

Corresponding Author: West Pomeranian University of Technology in Szczecin, Department of Electrical and Computer Engineering, ul. Sikorskiego 37, 70 313 Szczecin, Poland; E mail: [email protected].

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a)

b)

Figure 1. Photo of the measuring system: a) front panel, b) top view.

measurement system is introduced. We verify the performance of the system by measuring the depth of a defect in a flat titanium plate using a dedicated transducer.

1. ECT measuring system NDT systems in industrial applications have to be robust in that interference coming from various sources should not affect measurement results. The presence of noise in EC signals may mislead the flaw identification algorithms. This is important especially in the case of low testing frequency used for deeper material evaluation (greater penetration depth) which however cases week EC response signal (low signal-to-noise ratio). The most widely used noise suppression technique is digital filtering. It gives the best results if the signal can be separated from noises in a frequency domain. In many practical cases this condition is not fulfilled, and therefore filters may cause distortion of the original signals. It also affects the frequency characteristic. Therefore, a single frequency system with lock-in amplifier is proposed (Figure 1). Such system allows to detect signals caused by minor defects and having the amplitude lower than the noise level by extracting from whole spectrum only that signal’s component that has the same frequency as the excitation signal (reference signal). In consequence lockin technique allows to increase the sensitivity to minor flaws located deeper in the material. The proposed system allows to monitor amplitude and phase responses of a transducer using single testing frequency ranging from 1 kHz up to 100 kHz. The main part of the system is a lock-in amplifier based pick-up signal block. 1.1. Portable device of the system The block diagram of the measuring system is shown in Figure 2. A high speed 16-bit multifunction data acquisition converter (DAQ) with D/A and A/D modules (NI USB6251) are used in the system for both generating and acquiring signals. The DAQ device in connected via USB interface to the PC class computer which accumulates, computes data and controls the system. A generated in the D/A DAQ module sinusoidal signal is gained utilizing a high speed power amplifier (TDA 7294) before driving transducer's excitation coils. TDA 7294 is very low distortion and noise power amplifier with DMOS power stage. The driving current was controlled through LEM Components electronic transducer with no galvanic connection to the main circuit and was cut off if its value exceeds the maximum calculated for a measuring transducer.

T. Chady et al. / PLL Based Eddy Current Measuring System for Inspection of Outer Flaw

LIA BVD 150 H

NI 6251 REAL

LOCK IN

IMAG

SIGNAL IN

C/A TDA 7294

SWICH

TRANSDUCER

LOCK IN REF IN

DIGITAL OUT

PC COMPUTER

USB

A/C

251

POWER AMPLIFIER Figure 2. Block diagram of measuring system.

Induced voltage in the pickup coils are amplified by a programmable gain amplifier in lock-in LIA-BVD-150-H module [2]. It is a dual phase lock-in amplifier with digital phase shifter and detection of real component, imaginary component and amplitude of input signal. Such arrangement enables significant noise suppression. Lock-in amplifiers are commonly used to detect and measure very small AC signals - all the way down to a few nanovolts. Accurate measurements can be made even when the small signal is obscured by noise sources many thousands of times larger. Lock-in amplifiers use a technique known as phase-sensitive detection in order to separate real and imaginary components of a signal at a specific reference frequency and phase. Noise signals, at frequencies other than the reference frequency, are rejected and do not affect the measurement. Signals from lock-in module are then supplied to A/D DAQ module.

Figure 3. View of the LabView® environment software application.

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T. Chady et al. / PLL Based Eddy Current Measuring System for Inspection of Outer Flaw

The proposed system works with specialized software operating in the National Instruments' LabView environment. The software interface is shown in Figure 3. The application is used to drive the DAQ converter in order to control excitation instruments, configure PLL operating parameters (such as sensitivity and time constant) and acquire measuring signals (a real and imaginary part of measuring signal). All parameters of lock-in amplifier, DAQ and excitation signal can be introduced to the system through a configuration file. The application enables external and internal triggering of acquisition events. During the measurements, real time results of acquired signal, its absolute value, real and imaginary part, phase shift and finally plot of real versus imaginary part are presented to an operator. In the system there were three processing algorithms implemented utilizing statistical analysis, gradient and lowpass filtering. They allows to eliminate trends in the signal caused by the lift off and surface roughness. The algorithms compute correction values for a signal basing on value measured at present step and past ones and can be applied in-situ or after the measurements. 1.2. The transducer The transducer used in the system is presented in Figure 4. In order to make possible defect detection located 5 mm beneath the sample surface its dimensions (Figure 4b) and excitation frequency were optimized using FEM (Finite Element Method) and Comsol software. The transducer is built using an E-type ferrite core with excitation coils wound on exterior columns of the ferrite core and a pick-up coil on a central one. The excitation coils generate contrary directed fluxes in the pick-up coil. Therefore, the flux flowing through pick-up coil is close to zero in equilibrium state. If a flaw appearing close to one of the excitation coils distorts the generated flux flow, the signal different from zero is induced in the pick-up coil. Such configuration of the transducer allows us for the optimal usage of the dynamic range of the A/D converter module. In order to achieve the greatest equilibrium the excitation coils of the transducers were driven by separate power amplifier.

a)

b)

1 3

c) 4

44

1

5

2

25

3

2

Figure 4. Photo and view with dimensions of the transducer: a) photo of the transducer, b) 3D view of the transducer, c) photo of the transducers head; all dimensions are in [mm]; 1 ferrite core, 2 excitation coils, 3 pick up coil, 4 transducer head, 5 sample

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253

Figure 5. Photo and view of the titanium plate: a) photo, b) drawing of the notch, c) cross section drawing of the notch; x axis is the scanning axis

2. The verifying experiments The system is designated for the detection of minor outer flaws OF (casing discontinuity in the surface at the opposite site of the plate to the scanning side) in thick titanium specimens. In order to verify the performance of the proposed system several experiments were carried out. 2.1. Object of the experiment A titanium alloy plate having artificial EDM notches of different depth d was used (Figure 5.). The depth was ranging from 10 to 100% of the plate thickness (6.9 mm). All measurements were carried out for outer flaws. 2.2. Results of the experiment Results presented in the paper were obtained for 40% notch. First, the A-scan measurements using different exciting frequencies were carried out in order to find the optimal one. Figure 6 shows the results of real and imaginary component as well as amplitude and phase of the signal acquired during the experiments versus excitation frequency. From the set of achieved spectrograms one can notice that the frequency range between 8 and 16 kHz gives the greatest chance to detect the flaw. Considering result obtained for the real component of the signal (Figure 6a) it is clearly visible that frequency equal to 11.2 kHz is the optimal one. In the second stage of the experiments C-scan measurements were done. The two dimensional distribution of the signals amplitude measured in both scanning direction over selected area of 40% OF was presented in Figure 7a. In order to better visualize changes of signal caused by the flaw, plot of amplitude and phase shift as well as real and imaginary component of a signal measured in selected y line were shown in Figure 7b and Figure 8. The presented results allow easily to detect the flaw.

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T. Chady et al. / PLL Based Eddy Current Measuring System for Inspection of Outer Flaw

b)

f [kHz]

f [kHz]

a)

x [mm]

x [mm]

d)

f [kHz]

f [kHz]

c)

x [mm]

x [mm]

Figure 6. Multi frequency results of measurements obtained for 40% OF: a) real part of measured signal Re(Usig), b) imaginary part of measured signal Im(Usig), c) amplitude of measured signal |Usig|, d) phase of measured signal arctg(Im(Usig)/Re(Usig)).

b)

y [mm]

Usig [V]

a)

x [mm]

x [mm]

Figure 7. Single frequency results obtained for 40% OF: a) amplitude of signal |Usig| measured in selected area in both scanning direction, b) amplitude of signal |Usig| measured in selected y line.

3. Conclusions The newly developed ECT system for observation of minor defects in titanium alloy was presented. The system uses lock-in technique which allows to detect signals having the amplitude lower than the noise level by taking into consideration only that component of a signal which frequency is equal to the reference one. In consequence it

T. Chady et al. / PLL Based Eddy Current Measuring System for Inspection of Outer Flaw

b)

d)

x [mm]

arctg(Im(U)/ Re(U)) [rad]

x [mm]

Im(U) [V]

c)

Im(U) [V]

Re(U) [V]

a)

255

Re(U) [V]

x [mm]

Figure 8. Single frequency results of 1D scan obtained for 40% OF: a) real part of measured signal Re(Usig), b) imaginary part of measured signal Im(Usig), c) amplitude of measured signal |Usig|, d) phase of measured signal arctg(Im(Usig)/Re(Usig)).

leads to increase the possible depth penetration. The results of experiments with the titanium alloy plate having artificial notches confirm the possibility of using this system in industrial application. In the future, further experiments will be carried out for titanium discs with artificial flaws.

Acknowledgement This work was supported in part by Polish Ministry of Science and Higher Education and by European Commission sponsored project QualiTi which is a collaboration between the following organizations: I.S.O.TEST Engineering s.r.l, West Pomeranian University of Technology (ZUT), Tecnitest Ingenieros S.L., TIMET UK Ltd, TWI Ltd and Vermon SA. The project is co-ordinated and managed by TWI Ltd and is partly funded by the EC under the Research for the Benefit of Specific Groups Project (ref: FP7-SME-2007-1-GA-222476.)

References [1] National Transportation Safety Board Aircraft Accident Report NTSB AAR 98/01 [2] http://www.femto.de/datasheet/FEMTO_Product_Overview.pdf

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-256

Giant Magneto-Resistive Sensor based Magnetic Flux Leakage Technique for Inspection of Track Ropes W. Sharatchandra SINGH, B.P.C. RAO1, S. MAHADEVAN, T. JAYAKUMAR and Baldev RAJ Nondestructive Evaluation Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, TN-603102, India

Abstract. Giant magneto resistive (GMR) sensor based magnetic flux leakage (MFL) technique is proposed for detection of defects in 64 mm diameter track ropes. Helmholtz coil is used for magnetization and tangential component of leakage flux from defects is measured using a GMR sensor. This technique is able to detect local flaws and loss of metallic cross sectional area type defects in the track rope. Keywords. GMR sensor, magnetic flux leakage, track rope, finite element model

Introduction Steel wire ropes are used for material handling in mines and hauling of men in ski-lift operations [1]. In wire ropes, corrosion and wear are the main causes for damage such as formation of local flaws (LF) and loss of metallic cross-sectional area (LMA) [2-4]. LFs are external and internal discontinuities such as broken wires, cracks and corrosion pitting. Reasons for wire breaking can be due to fatigue, inter-strand nicking or martensitic embrittlement. LMAs are distributed defects such as missing of wires caused by corrosion, abrasion and wear resulting in loss of cross-sectional area. Periodic inspection of wire ropes is important to assess the structural integrity and to take corrective actions. Nondestructive inspection of wire ropes is challenging due to the heterogeneous structure of wire ropes, multiplicity, uncertainty of broken wires and hostile working environment. Visual and magnetic flux leakage (MFL) techniques are widely used for nondestructive inspection of wire ropes [4]. A variety of procedures that use different types of sensors and magnetizing devices have been employed for detection of defects in wire ropes by MFL technique [6-10]. Jomdecha et al. [7] used printed circuit-shaped coils connected in series as field sensors and solenoid as magnetization unit for inspection of wire ropes and reported detection of 2 mm deep surface defects in a 38 mm diameter wire rope. Kalwa et al. [9] developed an MFL system comprising of magnetic concentrators, Hall sensors and sensing coils and suggested that measurement of tangential component is more versatile than normal component for detection of multiple defects in wire ropes. 1

Corresponding Author: Dr. B.P.C. Rao, Head, EMSI Section, NDE Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, TN 603102, India, E mail: [email protected].

W.S. Singh et al. / GMR Sensor Based MFL Technique for Inspection of Track Ropes

257

In this paper, we propose MFL technique for detection of defects on the outer surface of 64 mm diameter track rope used for transportation of coal. The track ropes are stationary and are rigidly supported at periodic intervals. They are operated for about 10 hours every day transporting nearly 3000 tons of coal with the help of 256 numbers of stationary buckets each carrying nearly 1.6 tons of coal. The schematic of cross-section of the track rope is shown in Figure 1. The track rope has 8 layers of stranded wires of different diameters as detailed in Table 1. The width of the outer surface of the Z wire is 6.45 mm and the gap width between two outer Z wires is 0.76 mm. The carriage wheels of the bucket are in contact with the track rope and thus causing damage to the outer surface of the Z-wire. Service induced surface flaws are the major causes of failure in these ropes. When more than two Z wires of the outer layer are broken, they will be separated from the adjacent layers. Table 1 Track rope cross sectional details. Layer Wire details 1 2 3 4 5 6 7 8

1 centre wire 6 round wires 6 filler wires 12 round wires 18 round wires 13 round wires 32 Z wires 34 Z wires

Wire diameter or thickness, mm 4.00 4.66 1.93 4.33 4.27 4.95 5.50 6.48 Figure 1. Cross section of track rope.

Recently, GMR sensors are being widely used in MFL testing for detection of defects in carbon steel plates [10], pipelines [11] in view of their high sensitivity for low magnetic fields, good signal-to-noise ratio (SNR) and high spatial resolution. GMR sensors are attractive for measurement of feeble magnetic fields from shallow surface defects and deeply located sub-surface defects. They are also useful for detection of stress and fatigue damage [12]. This paper discusses MFL technique proposed using Helmholtz coil and GMR sensors for detection of defects in the track ropes. The results of the developmental studies carried out on artificial LFs and LMA defect in track rope are discussed. In order to interpret the measured MFL signal from LMA defect in the track rope, 3-D finite element modeling is performed and results are discussed.

1. GMR based MFL Technique 1.1. Measurement Set-up The schematic of the proposed MFL technique is shown in Figure 2. It consists of magnetization device, variable DC power supply, GMR sensor, track rope with defects, amplifier, and personal computer for data acquisition. The magnetization device consists of a Helmholtz coil with two circular coils of 70 turns each separated by 50 mm. The width and height of each coil are 20 mm and 15 mm respectively. The use of Helmholtz coil ensures uniform axial magnetization of the track rope. GMR sensor is

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W.S. Singh et al. / GMR Sensor Based MFL Technique for Inspection of Track Ropes

used for detection of tangential component (along the scan direction) of leakage flux from defects and is kept at the middle of the Helmholtz coil. Measurements are made by moving the GMR sensor and Helmholtz coil together as a single unit over the track rope in steps of 1 mm and at each axial location GMR sensor is scanned circumferentially. A constant lift off of 0.3 mm is maintained between the GMR sensor and the track rope to avoid physical damage to the sensor. In order to enhance the sensitivity of GMR sensor, its output is first amplified using a low-noise amplifier consisting of a differential amplifier, notch rejection filter at 50 Hz, 100 kHz low-pass filter and a single-ended variable gain amplifier with DC suppression. The variable gain amplifier is set such that it amplifies the sensor output 10 times. The amplified GMR sensor output is digitized using a 2-channel data acquisition system (16 bit) and stored in the computer for analysis. &RPSXWHU '&SRZHUVXSSO\

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Figure 2. GMR sensor based MFL testing set up.

1.2 GMR Sensor GMR sensor works on giant magneto-resistive effect in which there is a large drop in electrical resistance of the multilayer for an incident magnetic field due to spin dependent scattering of electrons at the interface between two ferromagnetic layers (few nm thick) separated by a nonmagnetic layer. The GMR bridge sensors (AA00302) manufactured by M/s NVE Associates are used. These sensors measure differential output voltage and ensure high stability with low noise (sensitivity ~260 VT -1 at 5V bias voltage). They exhibit linear response in 0.2-1.3 mT range followed by saturation. 1.3 Artificial Defects Localized flaws are simulated by introducing electro-discharge machined (EDM) notches on the outer surface of the track rope. Four axial (A, B, C, D) notches and four circumferential (E, F, G, H) notches of 5.5 mm length, 2 mm width and of different depths are machined as shown in Figure 3. The depths of the EDM notches measured using replica technique are given in Table 2. The distance between the notches is maintained at 80 mm which is slightly more than the length of Helmholtz magnetization unit. One LMA type defect is simulated by removing material (42.0 mm length, 9.2 mm width and 3.0 mm depth) from the outer surface of the Z wire and this is around 46% of the outer Z-wire (6.48 mm diameter).

259

W.S. Singh et al. / GMR Sensor Based MFL Technique for Inspection of Track Ropes



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Figure 3. Schematic of track rope having axial and circumferential machined artificial notches.

1.4 Magnetizing Current The magnetizing current in the Helmholtz coil is optimized such that detectable leakage field comes from all the notches. Current is optimized by studying the MFL signal peak amplitudes for shallow axial notches (A and C) and shallow circumferential notches (E and G). The signal amplitude is found to increase up to 6 A, beyond that it is decreased due to the penetration of significant amount of magnetic flux into the inner layer of the rope, as shown in Figure 4. Hence, a magnetizing current of 6 A is considered optimum and is used in this study.

GMR Signal Amplitude, V

2.5

2.05 mm deep axial notch (A) 5.86 mm deep axial notch (C) 1.94 mm deep circum. notch (E) 5.90 mm deep circum. notch (G)

2.0

1.5

1.0

0.5

0.0 0

2

4 6 8 Magnetizing Current, A

10

Figure 4. Optimization of magnetizing current.

2. Results and Discussion 2.1. LF defects GMR signals (tangential component of the leakage flux) of axial notches A, B, C and D are shown in Figure 5. The GMR sensor output for the shallowest axial notch (2.05 mm deep) is approximately 2.0 times the background noise that comes mainly from 0.76 mm wide stranded structure of the track rope. As can be observed all the four axial notches are detected by the technique with two distinct peaks correlated to the edges of axial notches. To access the detection and sizing capability of the technique, peak amplitude and Full Width at Half Maximum (FWHM) are determined after Gaussian fitting and interpolation and the results are shown in Table 2. The error in the

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determination of FWHM is ±0.1. As can be noted the amplitude of the MFL signals is found to increase with increase in notch depth. The FWHM is found to be nearly the same for all the axial notches, because of the constant notch length (5.5 mm). MFL signals of circumferential notches viz. E, F, G, and H are shown in Figure 6. The GMR response of circumferential notches is seen sharp with a single peak and the amplitude of 1.94 mm deep notch is 3.2 times the background noise. As can be seen from Figure 6, all the four notches are detected by this technique. The signal amplitude increases up to a depth of 5.90 mm and then decreases while the FWHM remains nearly constant (refer Table 2). It is observed from Table 2 that the amplitude of the circumferential notches is 2 to 3 times higher than that of axial notches of similar depth. However, the FWHM of circumferential notches is found to be nearly 2 to 3 times lower than that of the axial notches. These observations are due to the axial magnetization of the track rope causing circumferential notches to leak out higher flux in comparison to the extended axial notches. Using a simple threshold FWHM, it is possible to identify axial and circumferential defects in the track rope. Alternately, a set of array sensors covering the circumference can be used. 1 .2

C

A x ia l N o tc h e s

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S c a n D is ta n c e , m m

Figure 5. MFL signals of axial notches. 2.5 Circumferential Notches F

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Figure 6. MFL signals of circumferential notches.

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Table 2. The MFL signal amplitude and FWHM of axial and circumferential notches. Notch Notch Depth, mm Amplitude, V FWHM, mm A (axial) 2.05 0.58 4.8 B (axial) 4.11 0.91 5.5 C (axial) 5.86 1.22 4.8 D (axial) 7.91 1.25 4.6 E (circumferential) 1.94 1.86 1.8 F (circumferential) 3.88 2.33 1.6 G (circumferential) 5.90 2.56 2.0 H (circumferential) 8.24 2.50 1.7

The performance of the MFL technique is assessed for detection of a fine circumferential saw cut that simulates a fatigue crack in the track rope. The saw cut (length 15 mm, width 0.5 mm and depth 2 mm) and corresponding GMR sensor output are shown in Figure 7. Clearly GMR sensor has detected the saw cut. The signal amplitude nearly matches with the MFL signals of circumferential notches of Figure 6. The signal amplitude is found to be slightly less than the signal amplitude of circumferential notch E of similar depth due to smaller width of the former. Thus, this technique can be used for early detection of localized cracks in track ropes. In order to assess the resolution to multiple cracks, 5 saw cuts (C1, C2, C3, C4 and C5) are simulated with each of length 23 mm, width 1 mm and depth 2 mm, separated by a distance of 13.5 mm, 10.0 mm, 5.5 and 3.2 mm and the GMR sensor output is shown in Figure 8. As can be seen, the technique is able to detect all the 5 saw cuts and resolve the saw cuts separated by 3.2 mm distance. 2.2. LMA defects Photograph of LMA defect and its GMR sensor response are shown in Figure 9. The depth distribution (profile) of the LMA defect is measured using optical method. As can be observed, the GMR sensor has detected the LMA with good SNR.

1.2 1.0

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Figure 7. Photograph of a 2 mm deep saw cut in track rope and the measured GMR sensor output.

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C1

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Figure 8. Photograph of series of 2mm deep saw cuts machined in track rope and the corresponding measured GMR sensor output.

The LMA signal is found, as expected, extended as compared to the LF signal. There is a decrease in sensor output with respect to the baseline background, observed for the LMA defect. In order to understand this aspect, 3-D finite element modeling has been performed using COMSOL 3.4 Multiphysics software package. The model predicted tangential component of leakage field profile is also shown in Figure 9. In the model, the relative magnetic permeability and magnetization of the track rope are assumed as 100 and 106 A/m respectively. There is a good agreement between the measured and the model predicted signals and the decrease in signal amplitude for LMA defect appears to be due to the pulling of magnetic field lines into the track rope. Distance along LMA, mm 0

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Figure 9. Photograph of LMA (42.0 mm length, 9.2 mm width and 3.0 mm depth) machined in the track rope, GMR sensor response scanned along dotted line direction and optically measured depth profile.

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3. Conclusion GMR sensor based MFL technique has been proposed for detection of LF and LMA type of defects on the outer surface of 64 mm diameter track ropes. Performance of this technique has been validated by detecting a few saw-cuts and EDM notches simulating cracks in the track rope. For LMA type defects, a decrease in signal amplitude has been observed and confirmed by 3-D finite element model. This proposed MFL technique can be used for detection of both LF and LMA types of defects in track ropes. In order to further enhance the detection sensitivity and to implement the technique in field, work on the use of split type coils and array GMR sensors is underway.

4. Acknowledgements Authors thank Mr. S. Vaidyanathan and Mr. P. Krishnaiah, Electromagnetics, Modeling, Sensors and Imaging Section, NDE Division, Metallurgy and Materials Group, IGCAR, Kalpakkam for their help during the experiments.

References [1] S.S. Udpa and M.O. Patrick, ‘Nondestructive Testing Handbook - Electromagnetic Testing’, ASNT, 3rd Edition, Vol. 5, 2004, p. 437. [2] D. Basak, S. Pal and D. Chandra Patranabis, ‘In situ non destructive assessment of a haulage rope in a monocable zigback passenger ropeway’, Insight, Vol. 50, No. 3, March 2008, pp. 136 137. [3] Herbert R. Weischedel and R. P. Ramsey, ‘Electromagnetic testing, a reliable method for the inspection of wire ropes in service’, NDT International, June 1989, pp. 155 161. [4] Herbert R. Weischedel, ‘The Inspection of Wire Ropes in Service: A Critical Review’, Materials Evaluation, Vol. 43, December 1985, pp. 1592 1605. [5] N. Sumyong, A. Prateepasen and P. Kaewtrakulpong, ‘Influence of Scanning Velocity and Gap Distance on Magnetic Flux Leakage Measurement’, ECTI Transactions on Electrical Engineering, Electronics and Communications, Vol. 5, No. 1, February 2007. [6] E. Kalwa and K. Piekarski, ‘Design of Hall effect sensors for magnetic testing of steel ropes’, NDT International, Vol. 22, No. 5, October 1987, pp. 295 301. [7] C. Jomdecha and A. Prateepasen, ‘Design of modified electromagnetic main flux for steel wire rope inspection’, NDT&E International, Vol. 42, 2009, pp. 77 83. [8] Wang Hong yao, Hua Gang and Tian Jie, ‘Research on Detection Device for Broken Wires of Coal Mine Hoist Cable’, Journal of China University Mining & Technology, Vol. 17, No. 3, pp. 376 381. [9] E. Kalwa and K. Piekarski, ‘Design of inductive sensors for magnetic testing of steel ropes’, NDT International, Vol. 20, No. 6, December 1987, pp. 347 353. [10] W. Sharatchandra Singh, B. P. C. Rao, S. Vaidyanathan, T. Jayakumar and Baldev Raj, ‘Detection of Leakage Magnetic Flux from near side and far side Defects in Carbon Steel Plates using Giant magnetoresistive Sensor’, Measurement Science and Technology, Vol. 19, 2008 015702 (8pp). [11] L. Chen, P.W. Que and T. Jin, ‘A Giant Magnetoresistance Sensor for Magnetic Flux Leakage Nondestructive Testing of a Pipeline’, Russian Journal of NDT, Vol. 41, No.7, 2005, pp. 462 465. [12] T. Chady and G. Psuj, ‘Data fusion from multidirectional remanent flux leakage transducers for NDT of stress and fatigue loaded steel samples’, IEEE Trans. on Magn., Vol. 44, Nov. 2008, pp. 3285 3288.

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Application of Electromagnetic Nondestructive Techniques

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-267

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Pipe Wall Thickness Measurement by Electro-Magnetic Acoustic Transducer using Band Exciting Method Daigo KOSAKA a, Fumio KOJIMA b,1 and Kosuke UMETANI c Graduate School of Engineering, Kobe University, Kobe, Japan b Organization of Advanced Science and Technology, Kobe University, Kobe, Japan c Graduate School of System Informatics, Kobe University, Kobe, Japan a

Abstract. This paper is concerned with a quantitative nondestructive evaluation of pipe wall thinning using an Electro-Magnetic Acoustic Transducer (EMAT). First, two methods for sizing wall thickness, pulse-echo method (PEC) and electromagnetic resonance measurement technique (EMAR) are examined using calibration specimen of SS400. It was shown that EMAR is superior to PEC for its sizing accuracy. Secondly, we discuss a feasible measurement strategy based on EMAR technique. Finally, the feasibility studies of the method are summarized for evaluating mock Flow-Accelerated Corrosion (FAC) test samples. Keywords. Nondestructive test, Condition monitoring, Signal processing, Flowaccelerated corrosion

Introduction Phenomena of pipe wall thinning are critical issues on ageing management of nuclear power plants [1-7]. Pipe wall thinning management in nuclear power plants is aimed at providing a life management process ensuring replacement or repair prior to in-service failure. The main objective of pipe wall inspection is to identify the location of maximum thinning, to ascertain the extent and depth of the thinning, and to evaluate the wear rate. Currently the conventional technique is ultrasonic testing (UT) which provides the accurate resolution for the pipe wall thickness measurement. However, in UT, we must remove insulation from the piping area at each in-service inspection. There also exist so many inaccessible locations for the in-situ inspection by surveyors in practical plants. Therefore, continuous surveillance during operation is much more important than the periodical inspection by UT. Recently, we propose a monitoring technique of pipe wall thinning using Electro-Magnetic Acoustic Transducer (EMAT) [8]. EMAT is a non-contacting inspection device that generates an ultrasonic pulse in the sample inspected [9-13]. The advantage of our method is that measurements can be remotely implemented and the exciting test signals can be automatically reproduced by electrical circuits. EMAT consists of a magnet and a coil of wire and relies on electro-magnetic acoustic interaction for elastic wave generation. 1

Corresponding Author: Fumio KOJIMA, Organization of Advanced Science and Technology, Kobe University, 1-1 Rokkodai-cho, Nada-ku,Kobe 657-8501; Japan, E-mail: kojima@koala kobe-u.ac.jp

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Figure 1 illustrates our experimental apparatus. It is composed of EMAT, a burst power supply, an oscilloscope and a computer. A using sensor is shown in Figure 2. The sensor is a vertical type of EMAT which produces SH wave. The magnets generate a static magnetic field. The coil generates a dynamic magnetic field that induces eddy currents in a surface of a sample specimen. An ultrasonic wave is generated in the surface by the static magnetic field and the eddy currents. This type of sensor fits thickness measurement of pipe. There are two thickness measurement techniques for EMAT. Pulse-echo method (PEC) is a fundamental technique based on time domain approach. PEC is ease of use and rapid processing. However, unlike the conventional UT technique, the detecting signal by EMAT is not so large. Therefore, the use of PEC is not adequate for pipe wall thickness measurement. Electromagnetic resonance method (EMAR) is another thickness measurement technique based on frequency domain [14-15]. The method can estimate wall thickness from seeking a sequence of peak spectrums of detecting signals corresponding to sweeping frequencies of exciting test signals. Comparing that PEC method use one single frequency for exciting, measurement process by EMAR requires tedious treatment of signal processing. Nevertheless EMAR has advantages on the accurate resolution for sizing thickness of pipe. This paper is organized as follows: First, two measurement methods were compared in the point of thickness measurement method. Second, we propose a measurement method that uses an exciting voltage with a wide band. A receiving voltage of a wide band exciting voltage has information of with wide band frequency. This means this method is able to obtain the resonant frequency at one time. Finally, the method was applied to evaluate mock Flow-Accelerated Corrosion sample specimens.

Figure 1. Experimental setup.

Figure 2. Top view of EMAT.

1. Thickness measurement by EMAT Our experimental apparatus is composed of an EMAT, a pulser receiver, an oscilloscope, an auto stage and a computer. Burst waveform of the excitation voltage of 800Vpp is added to EMAT by pulsar. Two methods for sizing wall thickness are examined using calibration plate sample specimen of SS400.

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1.1. Pulse-echo method The pulsar signal was taken by two pulses with 2MHz. The reflective waveforms were recorded by a computer coupled to an oscilloscope. Using PEC, thickness calculation can be represented by

T=

vΔt 2

(1)

where T , v and ǻt denote thickness, sound velocity and time of flight (TOF). Sound velocity of SS400 is 3.216×103m/s. Detecting waveforms are shown in Figure 3. Figure 3(a) is a waveform of a plate sample specimen with 8mm thickness. Noting that the time of flight (TOF) ǻt was 4.9ȝs and from Eq. (1), the estimated thickness was taken as 7.9mm of which error became 0.1mm. Figure 3(b) is a waveform of a plate sample specimen with 6mm thickness. Since TOF was ǻt = 3.6ȝs, the estimated thickness was 5.8mm where the error was 0.2mm. Taking into account that TOF ǻt becomes proportional to the thickness, it is more difficult to recognize TOF ǻt for a smaller thickness.

Figure 3. Detecting waveforms using pulse-echo method.

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1.2. Resonance method EMAR utilizes collections of resonance frequencies by sweeping exciting voltages with wide frequency range. In our experiment, exciting time is 100ȝs, and exciting frequency range is 0.6MHz to 2.6MHz. The interval of the sweeping frequency was taken as 1kHz. For measurements by EMAR, the estimate of thickness can be derived from

T=

v 2Δf

(2)

where ǻf denotes a peak interval with respect to the frequency. The detecting waveforms of 4.7mm and 4.9mm thickness are shown in Figure 4. The ǻf is very clear that, if T is smaller, then the ǻt of pulse-echo method becomes smaller interval while the ǻf becomes larger interval. The ǻf of 4.7mm thickness and the ǻf of 4.9mm thickness are clearly distinguishable. This implies that EMAR method is more accurate measurement technique than PEC method. The ǻf of the detecting waveform of 4.7mm and 4.9mm thickness are 0.343MHz and 0.330MHz. Detecting thickness of the sample specimens is 4.69mm and 4.87mm. Figure 5 depicts the total resolution of the method presented here. In Figure 5, we admit the detecting accuracy was up to 0.1mm for SS400. On the other hand, measurement becomes time-consuming because EMAR requires sweeping exciting frequencies with wide range. In our experiment, each measurement spent about 2 minutes for obtaining sizing estimate.

Figure 4. Resonance frequency using EMAR method

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Figure 5. Thickness resolution of resonance method.

2. Measurement method using band exciting in EMAR In this section, we discuss a feasible measurement strategy for implementing EMAR method. As already suggested in the previous section, EMAR is time consuming in order to seek resonant state with wide frequency ranges. Figure 6 and 7 demonstrate one typical example for measurement strategy using an exciting waveform with a large frequency band. Figure 6, a frequency band of the exciting waveform was chosen from 0.9MHz to 1.8MHz. Then it was found that the detecting waveform in Figure 7 has some resonance frequencies at one shot. Hence we can reduce the measurement time by using a set of exciting signals with wide band.

Figure 6. Exciting waveform with wide band.

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Figure 7. Spectrums waveforms of band exciting method.

3. Application to pipe wall thickness measurement In this section, the band exciting resonance method is applied to evaluate a mock FAC sample specimen. As shown in Figure 8, a 6B-SS400 pipe was tested and the corrosion shape was fabricated to simulate flow accelerated corrosion (FAC). The extent of FAC was taken as 200 mm with the maximum thinning depth b = 1.0mm. Figure 9 shows estimating sizing results of the sample specimen by our measurement method. For the purpose of the comparative discussions, the conventional UT techniques were also performed.

Figure 8. Sample specimen of FAC model (a=160mm, b=1.0mm)

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Figure 9. Estimated sizing results for mock Flow-Accelerated Corrosion sample specimen.

4. Conclusions Two measurement methods for pipe wall thickness measurements were examined

using calibration specimen of SS400. It was shown that EMAR is superior to PEC for its sizing accuracy. It was shown that the measurement strategy using the exciting voltage with a wide band has achieved the rapid processing for thickness measurements. The feasibility studies of the method are summarized for evaluating mock Flow-Accelerated Corrosion (FAC) test samples. Detecting results of the method agreed well with detecting results of ultrasonic testing.

Acknowledgments This work has been performed as a part of the National Research Project for Enhancement of Measures against the Ageing of Nuclear Power Plants sponsored by the Nuclear and Industrial Safety Agency (NISA). The authors also gratefully acknowledge the Institute of Nuclear Safety System Inc. (INSS).

References [1] C. Schefski, J. Pietralik, T. Dyke, M. Lewis, A physical model to predict wear sites engendered by flowassisted corrosion, US DOE Rep, pp. 149-154, 1995. [2] B. Chexal et al., Flow-accelerated corrosion in power plants, EPRI report, TR-106611, 1996. [3] R. B. Dooley, V. K. Chexal, Flow-accelerated corrosion of pressure vessels in fossil plants, International Journal of Pressure Vessels and Piping, Volume 77, Issues 2-3, pp. 85-90, 2000. [4] Flow-accelerated corrosion in nuclear power plants: Application of CHECWORKS at Darlington, [5] T.R. Allen, P J. King, and L. Nelson: Flow Accelerated Corrosion and Cracking of Carbon Steel Piping in Primary Water Operating Experience at the Point Lepreau Generating Station, Proceedings of the 12th International Conference, pp. 773-784, 2005. [6] K. D. Efird, Flow accelerated corrosion testing basics, Pap Corros, p. 16, 2006. [7] S. Uchida, M. Naitoh, Y. Uehara, H. Okada, N. Hiranuma, W. Sugino, S. Kishizuka and D. H. Lster: Evaluation of Wall Thinning Rate with the Coupled Model of Static Electrochemical Analysis and Dynamic Double Oxide Layer Analysis, Journal of Nuclear Science and Technology Vol. 46, No. 1, pp. 31-40, 2009. [8] D. Kosaka, F. Kojima, H. Yamaguchi and K. Umetani, Monitoring System for Pipe Wall Thinning Management using Electromagnetic Acoustic Transducer, Vol.2, No. 1, pp.34-42, 2010.

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[9] H.M. Fros, Electromagnetic-ultrasonic transducer: Principles, practice and applications, in: Physical Acoustics, Vol. 14, W.P. Mason and R.N. Thurston eds., Academic Press, New York, pp. 179-275, 1979. [10] B.W. Maxfield and C M. Fortunko, The design and use of electromagnetic acoustic wave transducers, in: Material Evaluation, Vol.41, pp. 1399-1408, 1983. [11] R.B. Thompson, Physical principles of measurements with EMAT transducers, in: Physical Acoustics, Vol.19, Academic Press, New York, pp. 157-200, 1990. [12] K. Mirkhani et al. Optimal design of EMAT transmitters, in: NDT&E International, Vol. 37, pp. 181– 193, 2004. [13] D. MacLauchlan, S. Clark, B. Cox, T. Doyle, and B. Grimmett, Recent advancements in the application of EMATs to NDE, in: Proc. of the 16th WCNDT 2004, Montreal, Canada. [14] K. Kawashima, Very high frequency EMAT for resonant measurement, in: Proc IEEE Ultrasonic Symposium, No. 2, pp.1111-1119, 1994. [15] H. Ogi, “Field dependence of coupling efficiency between electromagnetic field and ultrasonic bulk waves”, J. Appl. Phys. 82 (8), 15, pp. 3940-3949, 1997.

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-275

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Applicability of Magnetic Flux Leakage Method for Wall Thinning Monitoring in Nuclear Power Plants Hiroaki KIKUCHI1, Isamu SHIMIZU, Katsuyuki ARA, Yasuhiro KAMADA and Satoru KOBAYASHI NDE & SR-C, Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka, Iwate, 020-8551, Japan Abstract. This paper presents an applicability of magnetic flux leakage (MFL) method for a nondestructive evaluation (NDE) of wall thinning in nuclear power plants. Since MFL method has already been applied to other industry field, this method should be an effective tool in nuclear power plants. The ancillary yoke poles were employed to adapt to the piping shape, and higher sensitivity was achieved to estimate the depth in a slit on piping. The distribution of magnetic flux density corresponding with profile of wall thinning depth was also obtained. Additionally, an applicability of MFL method for probing a slit fabricated on superposed specimens was investigated. Keywords. Wall thinning, magnetic flux leakage (MFL), ancillary yoke pole, reinforcing plate, dual layer

1. Introduction An ageing management for nuclear power plants is quite important issue due to its long-term operation in Japan. One of ageing problem is wall thinning on pipe. Wall thinning occurs at orifices, elbows and under reinforcing plates, etc., through FlowAccelerate Corrosion and Liquid Droplet Impingment erosion. Although several methods like ultrasonic, eddy current are available tools, the magnetic flux leakage (MFL) [1-4] also must be an effective nondestructive evaluation (NDE) technique for the wall thinning, because this method has already been applied to industry field such as gas pipeline. It is difficult to assess wall thinning under a reinforcing plate, where steels are superposed for reinforcements, using ultrasonic and eddy current, because of the reflection of signal and the wall thickness. Therefore MFL method is expected to apply for an evaluation of wall thinning under the reinforcing plate. The fundamental experiment of MFL using a single-yoke was examined and it was clarified that sizing of a rectangular slit fabricated on steel plates is possible [5]. However, a development of a probe feasible for piping and a feasibility study of MFL for application in a reinforcing plate are required for practical uses. Therefore, in this study, an applicability of MFL method for wall thinning monitoring in nuclear power plants was investigated, and a possibility to evaluate wall thinning under reinforcing 1

Corresponding Author: Hiroaki Kikuchi, NDE & Science Research Center, Faculty of Engineering, Iwate University, 4 3 5 Ueda, Morioka 020 8551, Japan; Phone:+81 19 621 6890; Email: hkiku@iwate u.ac.jp

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plates using MFL was examined. The ancillary yoke poles were utilized to solve the problem in contact between the magnetic-yoke and the pipe surface and to achieve higher sensitivity for estimation of slit depth on piping. Additionally, steels superposed were prepared and a slit modeled wall thinning was formed in underlayer, then an evaluation of the slit was performed using MFL method.

2. Utilization of ancillary yoke pole 2.1 FEM analysis Firstly, to confirm an effect of ancillary yoke pole, two-dimensional (2D) FEM analysis was done. Figure 1(a) shows the analysis model for the calculation. Since a conventional magnetic-yoke has a flat plane on contact part, there is a large air gap between the yoke and the surface of the pipe. The magnetic flux density distribution was calculated along with the dot line shown in Figure 1(a) when the pipe has a slit with 10 mm width and 2 mm depth and when the pipe has also no slit. The calculation was done for both x- and z-components of magnetic flux density, Bx, By. An applied current to the excitation coil was 1 A. Figure 2 shows the calculated results. The results show the same behavior in both cases being independent of existence of slit. This means detection of a slit on pipe is difficult if there is a large air gap between the yoke and the pipe surface. Figure 1(b) shows the FEM analysis model when ferromagnetic material exists between the yoke and the surface of the pipe as ancillary yoke poles. The distribution of both x- and z-components, Bx, By, of magnetic flux density was calculated along with the dot line shown in Figure 1(b). Figure 3 shows those calculated field distributions. One can see the notable difference in both distribution profiles. These calculated results indicate the ancillary yoke pole is very useful to achieve higher sensitivity. 2.2 Experimental procedure Figure 4(a) shows the dimension of the magnetic-yoke used for experimental investigating the utilization of ancillary yoke poles. The geometry and the size of the specimen are shown in Figure 5. The diameter is 60.5 mm and thickness is 5.2 mm, and carbon steel STPT is used for their material. A slit with 10 mm width is fabricated at Conventional yoke Coil: 1000 T

Air gap

Conventional yoke Coil: 1000 T

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Silicon Iron

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(a) with air gap (b) using ancillary yokes Figure 1. 2D FEM analysis model.

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(a) x component, Bx (b) z component, Bz Figure 2. Leakage magnetic flux density distribution with air gap between yoke and pipe. 100 without slit with slit

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(a) x component, Bx (b) z component, Bz Figure 3. Leakage magnetic flux density distribution with ancillary yokes between yoke and pipe.

the center part of the pipes, and its depths are 0.5, 1, 4, 4.5 mm, respectively. The coordinate for measurement system is defined as shown in Figure 4(a). The center part of slit is the origin of x-direction (horizontal), and the vertical direction to horizontal is z-direction (the surface of specimen is z = 0). Figure 4 (b) shows the geometry and the size of ancillary yoke pole adjusted for the pipe shown in Figure 5. The material for this pole is pure iron. To obtain soft magnetic properties, the pole was annealed at 700 ƷC for 1 hour in the atmosphere after its machining. After annealing, the poles were polished to remove oxide layer. 2.3 Results Figure 6 plots x- and z- component of magnetic flux density, Bx, Bz against position x (Here, center of the slit is x = 0). On the measurement, the applied current to the excitation coil was 3 A, and the magnetic-yoke was fixed as the center of the yoke corresponding with the center of the slit, and a gauss meter (Lakeshore 460) scanned the pipe surface in x-direction at z = 0.5 mm. The pipes with slit depth of 4 and 4.5 mm were used here. The results obtained with ancillary yoke poles are shown as compared with measurement without ancillary yoke poles. It is clarified that the higher sensitivity was obtained when the ancillary yoke poles were used. As for the pipe with slit depth of 4 mm, the intensity of Bx has no change and Bz has no peak at the edge of slit in the case without ancillary yoke poles, while the profile using ancillary yoke poles shows large increment in Bx profile and has a peak in Bz at the edge of slit (x = 5 mm). For the

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Figure 4. Measuring system for MFL and dimensions of magnetic yoke and ancillary yoke pole. Wall thinning

d

w

10 mm

60.5mm

t = 5.2mm

# 2345mm

Wall thinning

60mm

Figure 5. Dimension of pipe with slit. 200 Magnetic flux density Bz (Gauss)

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14

-2

0

2

4 6 8 10 Position x (mm)

12

14

(a) x component, Bx (b) z component, Bz Figure 6. Experimental leakage magnetic flux density distribution with and without ancillary yoke poles between yoke and pipe (AY: with ancillary yoke, NAY: without ancillary yoke).

pipe with slit depth of 4.5 mm, the changes in Bx and the peak intensity in Bz at x = 5 mm were enhanced using ancillary yoke poles. Figure 7 plots x- and z- component of magnetic flux density, Bx, Bz against position x, when the probe includes the magnetic-yoke, ancillary yoke poles and the gauss meter scanned the pipe surface in x-direction (In this case, gauss meter and magnetic-yoke scanned together). The depth of slit changes from 0.5 to 4.5 mm. The xcomponent Bx of flux has rapid increase at x = 5 mm, and its rate of change increases with increasing slit depth. On the other hand, the z-component Bz of flux has a peak at x = 5 mm, and its intensity increases with increasing depth of slit. The position x = 5 mm is consistent with the edge of slit.

3. Evaluation of wall thinning on pipe Pipe specimens with modeled wall thinning being similar to the practical cases were

H. Kikuchi et al. / Applicability of Magnetic Flux Leakage Method for Wall Thinning Monitoring 300 Magnetic flux density Bz (Gauss)

Magnetic flux density Bx (Gauss)

-20

279

-40 -60 -80 -100 -120 d = 0.5 mm d = 1 mm d = 4 mm d = 4.5 mm

-140 -160 -180

d = 0.5 mm d = 1 mm d = 4 mm d = 4.5 mm

250 200 150 100 50 0 -50

-5

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5 10 15 Position x (mm)

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25

-5

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20

25

(a) x component, Bx (b) z component, Bz Figure 7. Experimental leakage magnetic flux density distribution with ancillary yoke poles, when slit depth d changes. 60

20

14

57

Figure 8. Dimension of pipe with wall thinning. a is maximum depth, b width of slit and ' central angle of wall thinning part.

63.4㫦

Unit: mm

Figure 9. Dimension of ancillary yoke pole.

prepared, and MFL method using ancillary yoke poles was examined to assess wall thinning of those specimens, here. The configuration and the size of pipe are shown in Figure 8. Its diameter is 114.3 mm and its thickness is 8.6 mm, respectively. The material of the pipe is carbon steel STPG. We prepared two specimens, A and B. The value of a, b and ' shown in Figure 8 are 4.4 mm, 100 mm, 130 deg., respectively for specimen A, and those values for specimen B are 2.15 mm, 50 mm, 90 deg., respectively. The magnetic-yoke used here was the same as mentioned in Figure 1 (a), while another ancillary yoke poles adjusted for the pipe shown in Figure 8 were prepared. Figure 9 shows the geometry and the size of ancillary yoke pole. The gauss meter was fixed at the center part of the magnetic-yoke, and the magnetic-yoke with the ancillary yoke poles scanned the pipe surface in x-direction. The x- component of magnetic flux density, Bx was measured with application of 3 A current to the excitation coil. The scans were performed along with the line passing through the deepest wall thinning point in both A and B specimens and were also performed along with the line passing through out of wall thinning area; this means scanning excludes wall thinning part. Figure 10 shows the distribution of x- component of magnetic flux density Bx against position x. For both specimen A and B, magnetic flux density is constant on the line passing through out of wall thinning area, while the distributions on the line passing through deepest wall thinning point reflect the depth profiles of wall thinning in each specimen (the cases of A: a = 4.4 mm and B: b = 2.15 mm). The magnetic flux density at deepest wall thinning point in specimen A is larger than that of specimen B. At deeper wall thinning point, larger magnetic flux density is obtained.

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Magnetic flux density Bx (Gauss)

40 Specimen A: Wall thinning area 35

30 Specimen B: Wall thinning area

25

A A B B

20 -100

-50

a 4 4 mm line out of slit a 2 15 mm line out of slit

0 50 Position x (mm)

100

Figure 10. Experimental leakage magnetic flux density distribution for pipe with modeled wall thinning.

Excitation coil 150 turns

Unit: mm 80

20

Gauss meter 6

45

z Bz

Scan Bx x

0

Specimen

10

d

6

Figure 11. Measurement setup for investigation of dual layered specimen.

4. Evaluation of slit on dual layered specimen Here, we investigated an applicability of MFL method to an evaluation of wall thinning under the reinforcing plate. As a feasibility study, we tried to detect a slit fabricated at the underlayer of superposed plates using MFL method. Figure 11 shows the measurement system for evaluation on dual layered specimen (superposed plates). The magnetic-yoke the same as described in section 2 was located on the superposed specimen with a slit (10 mm width) on its underlayer. Each plate had 6 mm thick, and total thickness was 12 mm. The yoke and the gauss meter scanned together in x-direction (See Figure 11), and measured the x- and zcomponent of magnetic flux density, Bx, Bz, on the surface of specimen when the slit depth d changed from 1 to 3 mm. Figure 12 plots the value of Bx, Bz against position x. For all specimens, Bx has the maximum at x = 0 and a rapid change rate in Bx was obtained at x = 5 mm. The intensity of Bx at x = 0 and change rate in Bx at x = 5 mm increase with increasing slit depth. On the other hand, Bz has a peak at 5 mm where it is consistent with the edge of slit and the peak intensity increases with increasing slit depth. These results indicate MFL method is applicable to detection of slit formed in the superposed specimen, that is, applicable to evaluation of wall thinning under reinforcing plate.

H. Kikuchi et al. / Applicability of Magnetic Flux Leakage Method for Wall Thinning Monitoring 40 no slit d 1 mm d 2 mm d 3 mm

55 50

Magnetic flux density Bz (Gauss)

Magnetic flux density Bx (Gauss)

60

45 40 35 30 25 20 -20 -15 -10

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-5 0 5 10 Position x (mm)

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no slit d 1 mm d 2 mm d 3 mm

10 0 -10 -20 -30 -40 -20 -15 -10

-5 0 5 10 Position x (mm)

15

20

(a) x component, Bx (b) z component, Bz Figure 12. Relations between magnetic flux density and position x, when slit depth d changes.

5. Conclusion In order to accommodate the shell structure of pipe, ancillary yoke poles are adopted, and probing of slit and wall thinning on pipe was performed. Additionally, detection of slit fabricated on dual layered specimen was examined as a feasibility study of evaluation of wall thinning under reinforced plate. The following results were obtained. (1) It was clarified the evaluation for wall thinning on pipe using MFL method is possible. (2) The higher sensitivity was achieved with ancillary yoke poles. (3) The capability of evaluation of wall thinning on dual layer was performed; this indicates MFL method can be applied for evaluation of wall thinning under reinforcing plate. (4) Output distributions corresponding with wall thinning depth on specimen being similar with actual cases were obtained.

Acknowledgment This work is supported by Nuclear and Industrial Safety Agency Project on Enhance of Ageing Management and Maintenance of Nuclear Power Plants.

References [1] C. E. Edwards, S. B. Palmer, The magnetic leakage field of surface breaking cracks, Journal of Physics D: Applied Physics, 19, pp. 657 673 (1986). [2] K. Sekine, Present Status and Some Problems in Defect Evaluation Using Magnetic Inspection, Tetsu- toHagane, 74, pp. 2231 2238 (1988). [3] T. Suzuki, Electromagnetic Simulation Technique for Magnetic Leakage Flux Testing, Journal of the Japanese Society for Non-destructive Inspection, 47, pp. 92 97 (1998). [4] Y. Zhang, G. Yan, Detection of Gas Pipe Wall Thickness Based on Electromagnetic Flux Leakage, Russian Journal of Nondestructive Testing, 43, pp. 123 132 (2007). [5] H. Kikuchi, Y. Kurisawa, Y. Kamada and S. Kobayashi, K. Ara, International Journal of Applied Electromagnetics and Mechanics, 33, pp. 1087 1094 (2010).

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Stress Corrosion Cracks Evaluation in 316 Austenitic Stainless Steel Plate Tomasz CHADY1, Jacek KOWALCZYK, Grzegorz PSUJ Department of Electrical and Computer Engineering, West Pomeranian University of Technology, al. Piastow 17, 70-310 Szczecin, Poland

Abstract. In this paper a ECT system was used to inspect stress corrosion cracks (SCC). The system utilizes lock in amplifier, which enables observation of signals having the amplitude lower than the noise level. The sample with three SCCs examined during test was made of 16 mm thick 316 austenitic stainless steel. Keywords. Eddy current testing, stress corrosion cracks

Introduction Nowadays, evaluation of stress corrosion cracks (SCC) in real construction is one of the most important problems. The SCC strongly affects the structural integrity of the material. Furthermore, there are many differences between SCC and artificial notches in their responses to nondestructive testing (NDT) methods. Therefore the notches cannot be used as a substitute of SCC during evaluation of the NDT system performance. This creates strong and obvious need of fabricating cracks more equivalent to real one. On this background, the Japan Society of Maintenology has started round-robin tests under SCC NDT database Project [1]. Some works on the methodology of artificial SCC preparation and observation have been published [2-4]. The round–robin test creates opportunity to evaluate quality of the measurements achieved with various techniques. Objective of this paper is to present results obtained by using ECT multi-frequency technique and system equipped with a lock-in amplifier. The advantages of the lock-in amplifiers like high noise immunity, precise estimation of real and imaginary part of the measured signals allows to detect defects with a higher precision.

1. Experimental setup In the experiments lock-in ECT system was used and the three stress corrosion cracks were examined. The details of the system and the sample tested will be given below. The utilized system is an integrated unit. It allows to monitor amplitude and phase responses of a transducer. The system can operate using single frequency ranging from 1 kHz up to 100 kHz. It consists of excitation, pick-up and control subsystem.

1

Tomasz Chady, email: [email protected]

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Figure 1. Photo and view of the transducer: a) 3D view of the transducer, c) photo of the transducers.

The excitation subsystem uses D/A converter and high speed power amplifier (TDA 7294) for generation and gaining sinusoidal current. The main part of the system is a lock-in amplifier based pick-up system. Voltage induced in the pickup coils are amplified by a programmable gain amplifier in the lock-in LIA-BVD-150-H module. The LIA-BVD-150-H is dual phase lock-in amplifier with digital phase shifter and detection of real component, imaginary component and amplitude of input signal. Signals from the lock-in module are then supplied to an A/D module. Both subsystems are controlled by a PC class computer with software written in LabView® environment. The transducer was moved over the sample using a X, Y, Z scanning device. The transducer used during the measurements consists of a ferrite core (6) with five symmetrically placed columns [5]. The view and photo of the transducer is shown in Figure1. Pick-up coil (5) is wounded on the central column. Four excitation coils (1, 2, 3 and 4) placed on remaining columns are divided into two sections perpendicular to each other. Each section consists of two excitation coils connected in series and produce in the pickup coil opposite (to another pair) directed fluxes, which induce in the pick-up coil a signal close to zero in equilibrium state. The flaw occurring close to one of the excitation coils distorts that state and therefore a signal different from zero appears in the pick-up coil. 1.1. SCC samples The sample TP01 used in the experiment belong to the round robin test organized by the Japan Society of Maintenology. It is made of 316 austenitic stainless steel. The dimensions of TP01 are 160 mm long, 100 mm width and 16 mm thick. The sample is having three stress corrosion cracks: SCC01-1, SCC01-2, and SCC01-3. Detailed description of SCC fabrication can be found in [1-4]. The distance between two neighboring cracks is about 30 mm. Surface lengths of the cracks evaluated using penetrant testing (PT) technique are 26, 28 and 29 mm. Detail information about the specimen can be found elsewhere [1].

2. Results of Experiments The experiment was divided into two stages. During the first one, stress corrosion cracks were scanned along one line. Different excitation frequencies were used for each scan. The frequency range was between 70 kHz and 88 kHz with step of 2kHz. Figure 2 and Figure 3 show the results of multi-frequency experiments. The transmitter was moved perpendicular to the direction of the defects and above their centers.

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x [mm]

f)

x [mm]

f [kHz]

x [mm]

f [kHz]

e)

d)

f [kHz]

x [mm]

f [kHz]

c)

f [kHz]

b)

f [kHz]

a)

x [mm]

x [mm]

h)

U [V]

arctg(Im(U)/Re(U)) [rad]

g)

x [mm]

x [mm]

Figure 2. Multi frequency results of measurements obtained for SCC01 1(a) amplitude and b) phase of the measured signal), SCC01 2 (c) amplitude and d) phase of the measured signal) and SCC01 3 (e) amplitude and f) phase of the measured signal); plot of amplitude (g) and phase (h) of signals obtained for all SCCs using exciting frequency equal to 82 kHz .

T. Chady et al. / Stress Corrosion Cracks Evaluation in 316 Austenitic Stainless Steel Plate

x [mm]

f)

x [mm]

f [kHz]

x [mm]

f [kHz]

e)

d)

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x [mm]

f [kHz]

c)

f [kHz]

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f [kHz]

a)

285

x [mm]

x [mm]

h)

Im(U) [V]

Re(U) [V]

g)

x [mm]

x [mm]

Figure 3. Multi frequency results of measurements obtained for SCC01 1(a) real and b) imaginary component of the measured signal), SCC01 2 (c) real and d) imaginary component of the measured signal) and SCC01 3 (e) real and f) imaginary of the measured signal); plot of real (g) and imaginary component (h) of signals obtained for all SCCs using exciting frequency equal to 82 kHz .

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y [mm]

One can see that all results allow proper indication of the SCC in the sample. There are only slight differences in measured amplitude and phase of signals as well as in real and imaginary components of signals obtained for each frequency.

x [mm] Figure 4. Amplitude of signal |Usig| measured in selected area of SCC01 1 in both scanning direction using exciting frequency equal to 82 kHz.

b)

U [kHz]

arctg(Im(U)/Re(U)) [rad]

a)

x [mm]

x [mm]

d)

Im(U) [V]

Re(U) [V]

c)

x [mm]

x [mm]

Figure 5. Results of measurements obtained for selected line scan of SCC01 1 using exciting frequency of 82 kHz: a) amplitude of measured signal |Usig|, b) phase of measured signal arctg(Im(Usig)/Re(Usig)), c) real part of measured signal Re(Usig), d) imaginary part of measured signal Im(Usig).

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Nevertheless, the highest amplitude was observed in case of the exciting frequency of 82 kHz. It creates the greatest possibility of proper indication of SCC. From the Figure 2 g-h and Figure3 g-h one can observe that response of SCC01-1 is the highest and of SCC01-3 is the smallest, which is confirmed by the results achieved by other research teams [1]. In the second stage of experiments the measurements for SCC01-1 in both directions x and y using exciting frequency equal to 82 kHz were carried out. The achieved results are presented in Figure 4 and Figure 5. Figure 4 shows a twodimensional plot of amplitude of the measured signal and Figure 5 plots of amplitude and phase of a signal as well as real and imaginary component of a signal for selected line scan.

3. Conclusions The results of the experiments show the possibility of usage of the lock-in ECT system for evaluation of SCC in stainless steels. The highest signals parameters and signals components were achieved for SCC01-1. The results are not yet verified by destructive tests, however similar conclusions were presented by other institutions examining the sample.

Acknowledgements The authors would like to thank Dr Noritaka Yusa for providing the specimens that belong to the round robin test organized by the Japan Society of Maintenology (http://jsm.or.jp/at/scc/). This work was supported in part by Polish Ministry of Science and Higher Education and by European Commission sponsored project QualiTi which is a collaboration between the following organizations: I.S.O.TEST Engineering s.r.l, West Pomeranian University of Technology (ZUT), Tecnitest Ingenieros S.L., TIMET UK Ltd, TWI Ltd and Vermon SA. The project is co-ordinated and managed by TWI Ltd and is partly funded by the EC under the Research for the Benefit of Specific Groups Project (ref: FP7-SME-2007-1-GA-222476.)

References [1] SCC NDT database Project, The Japan Society of Maintenology, online access, http://jsm.or.jp/jsm/at/scc/index_eng.htm [2] N. Yusa, S. Perrin, K. Miya, Eddy current data characterizing less volumetric stress corrosion cracking in nonmagnetic materials, Matterials Letters 61 (2007), 827 829 [3] N. Yusaa, H. Hashizume, Evaluation of stress corrosion cracking as a function of its resistance to eddy currents, Nuclear Engineering and Design 239 (2009) 2713 2718 [4] N. Yusa, K. Miya, Discussion on the equivalent conductivity and resistance of stress corrosion cracks in eddy current simulations, NDT&E International 42 (2009) 9 15 [5] T. Chady, Evaluation of Stress Loaded Steel Samples Using Selected Electromagnetic Methods, Review of Progress in Quantitative Nondestructive Evaluation, vol. 23A, D.O. Thompson, D.E.Chimenti, American Institute of Physics, 2004, pp. 1296 1302

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Multi-frequency eddy current NDE of the distance between parts in aeronautical assemblies Thanh Long CUNG, Pierre Yves JOUBERT and Eric VOURC’H SATIE, ENS Cachan, CNRS, UniverSud, 61 avenue du Président Wilson, 94235 Cachan Cedex, France

Abstract. This paper deals with the eddy current nondestructive evaluation of the distance between parts in metallic assemblies. An experimental study of the coupling of a magnetic cup core coil sensor with a metallic layered structure is carried out and confirmed by finite element modeling simulations. This study allows behavioral models of the sensor/structure interactions to be built, and two estimation methods to be proposed. The first one is based on the inversion of a polynomial forward model, and the second one on an inverse model. Both techniques are implemented, characterized and compared. The second one is proved to be more accurate when the signal to noise ratio of the eddy current data decreases.

Keywords. Non-destructive evaluation, eddy currents, multi-frequency approach, air gap estimation, multilayered aeronautical structure, behavioral inverse model

Introduction The eddy current technique (EC) is widely used for the NDE of electrically conducting parts, such as those that may be found in the aeronautic industry. Indeed, it is easy to implement, sensitive, robust and eco-aware. Under certain conditions, it allows defects [1-3] or geometrical/physical features [4] of the inspected parts to be evaluated with satisfactory accuracy. However, the quantitative evaluation of parts parameters starting from the raw EC data is generally known as an "ill-posed" problem, among other reasons because of the incompleteness of the available EC data [5]. This remark particularly applies to the evaluation of multilayered structures such as aeronautical assemblies, which is known to be particularly difficult [6]. To solve this particular problem, several methods have been proposed, such as the inversion of a physical model of the impedance of an air coil, using the least mean square criterion. Another solution relies on the use of gradient techniques or neural networks [7]. Another possibility consists in an experimental approach in which the experimental data are directly differentiated from measurements simultaneously carried out on a series of calibrated mock-ups [6]. In this paper, we propose to build multi-frequency behavioral models, based on experimental analyses of the interactions between a cup-core EC sensor and a multilayered assembly. This technique has the advantage of being applicable to any type of EC sensor and to be easy to implement, once the model developed. Moreover, the multi-frequency approach allows the available EC data to be enriched so as to increase the reliability and the accuracy of the NDE [1]. In this study,

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we consider the problem of evaluating the thickness of an air layer comprised between two conductive plates, representative of a metallic coating assembled to ribs or spars in aircraft wings. Section 1 both reports on the experimental setup and on the analysis of the interactions between the used sensor and a layered structure. In Section 2, a polynomial based modeling is derived from this analysis and inversion results are presented. In Section 3, we propose and implement a behavioral inverse model associated to a multi-frequency evaluation algorithm. Evaluations results are compared and concluding remarks are given in section 4.

1. Experimental study of the problem 1.1. Experimental setup In the experimental setup, the wing coating is represented by a plate of constant thickness tc = 1.5 mm, whereas the rib which in practice is a piece of variable thickness, is represented by a series of plates featuring thicknesses comprised between 1.5 mm and 25 mm. Both the coating and the rib are made of an aluminum alloy featuring an electrical conductivity σ = 17 MS/m and a unitary relative magnetic permeability. To adjust the distance between the conductive layers, calibrated isolating sheets are used. They feature a unitary relative magnetic permeability and a unitary relative dielectric permittivity. The resulting distance between the conductive layers, or air-gap thickness, denoted t, is comprised in the [0 μm 500 μm] range. The EC NDE is performed by means of a magnetic cup-core coil probe electromagnetically coupled to the assembly, as shown in Figure 1. The coil features 110 turns and an outer diameter of 35 mm. Its free impedance (obtained when the sensor is not coupled with the target) is equivalent to a resistance R0 = 4.6 Ω in series with an inductance L0 = 3.04 mH. EC data are provided through the measurement of the sensor impedance via a PC controlled impedance analyzer (HP4192A). More precisely, we consider the sensor normalized impedance denoted Zn and defined as [4]:

Zn = Rn + j.X n = (Zt − R0 ) / X 0

(1)

where Zt is the impedance of the sensor coupled with the assembly featuring a given air gap t, and X0 is the reactance of the uncoupled sensor.

Figure 1. Eddy current cup core coil sensor coupled with the inspected multilayered assembly.

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Figure 2. Universal impedance diagrams of the EC sensor: a) general view, and b) detailed view for Znt with t ranging from 0 to 500 μm.

1.2. Sensor and target interactions The properties of the universal impedance diagram (UID), i.e. the evolution of Zn in the complex impedance plane (Rn, Xn), have been studied [4, 8] in the case of a bulk target. It is used here to evaluate the assembly. As an example, the UIDs obtained for two assemblies featured by t = 0 μm (close to a bulk target) and t = 500 μm, are presented in Figure 2a over an 80 Hz to 30 kHz frequency range. These UIDs show that there exists a frequency range in which the properties of the measured EC data are likely to allow t to be evaluated. The UIDs plotted in that frequency range are represented in Figure 2b, for parts separated from 0 to 500 μm. Indeed, the locus of the points obtained at the same frequency but for different distances t (tc and tr being fixed) is a linear curve. This result led us to analyze the relationship between t and a normalized impedance distance (NID) defined as (2). NID f i = Z nt ( f i ) − Z n 0 ( f i )

(2)

where fi is the considered EC frequency, Zn0 and Znt are the normalized impedance of the sensor for t = 0 and t  0 respectively. Experimentally, it appears that a linear equation relates NID to t (3), provided that the frequency f does not exceed a maximum value fmax, fmax being such that the skin depth δ of the induced EC approximately equals 2/3rds of tc.

NID ( t ) = a ( f , tc , tr ) t

(3)

The slopes of the linear characteristics (3) depend on the frequency, the coating and the rib thicknesses, as shown in Figure 3 for the following configurations: f1 = 680 Hz, f2 = 6600 Hz, tr1 = 1.5 mm, tr2 = 25 mm, and tc = 1.5 mm. As a result, equation (4), which is established at a single frequency f1, is not sufficient to estimate t for an unknown value of the thickness tr. Therefore, a multi-frequency approach is required.

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Figure 3. Linear relationship between NID and the air-gap thickness t −1

ti = a f i .NID f i

(4)

2. Estimation method relying on a polynomial forward model

2.1. Inversion of a polynomial forward model (IPFM) In order to build a multi-frequency forward model of NID as a function of t, tc, and tr, we use a second order polynomial of the variables t and tr expressed in (5). Such a small order is chosen with inversion accuracy in view [9].

NID f i (t , t r ) = t ( c0, f i + c1, f i t r + c2, f i t r2 )

(5)

where the coefficients {c0,fi , ... c2,fi} are such that for a fixed value of tr, NIDfi be a linear function of t, according to (2), with NIDfi (0,tr) = 0. To determine the coefficients of (5), we use the data resulting from a series of FE simulations of the sensor coupled with a layered structure featuring tc = 1.5 mm, tr ∈ {1.5, 2.0, 2.5, 3.0, 3.5}, given in mm, t ∈ {100, 200, 300, 400, 500}, given in μm and with a set of five frequencies fi (i∈{1,2,3,4,5}) given in Hz: f1 = 680, f2 = 1060, f3 = 1440, f4 = 1820, f5 = 2200. These data constitute the learning set used to determine the polynomials of the forward model at each considered fi frequency, by the means of a least mean square criterion. The multi-frequency forward modeling of NID then writes:

n = Ct

(6)

where n is the column vector of the NIDfi elements, C is the matrix of the {c0,fi , ... c2,fi} coefficients, and t = [t, ttr , ttr2 ]T . Consequently the estimation of t and tr is given by (7).

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t = (CT ⋅ C ) ⋅ CT ⋅ n −1

(7)

2.2. Estimation results The estimation based on the IPFM is implemented and evaluated using computed and experimental data. In order to better evaluate the estimation performances, additional white and Gaussian noise of various powers have been added to the simulated data so as to introduce some uncertainty representative of instrumental noise and sensor mispositioning errors [11]. Table 1. RAE and RPE of the air layer thickness estimation obtained using the IPFM and different frequency combinations. (*) Meaningless values of RAE or RPE (> 100 %). Assembly configurations tc = 1.5 mm ; tr = 1.5 mm ; t ∈ {0, 50, 100, 150, ...500) in μm IPFM using fi IPFM using fi IPFM using fi Data i∈ {2,3,4,5} i∈ {1,2,3,4,5} i∈ {2,3,4} (RPE% ; RAE%) (RPE% ; RAE%) (RPE% ; RAE%) Comput.(SNR = 60 dB) 0.77 ; (*) 13.20 ; 1.20 1.24 ; 0.42 Comput. (SNR = 33 dB) 17.25 ; (*) 75.00 ; (*) 28.02 ; -0.20 Experim.(SNR=33 dB) 40.44 ; (*) (*) ; (*) 49.16 ; -19.21 Assembly configurations tc = 1.5 mm ; tr = 3.5 mm ; t ∈ {0, 50, 100, 150, ...500) in μm IPFM using fi IPFM using fi IPFM using fi Data i∈ {2,3,4,5} i∈ {1,2,3,4,5} i∈ {2,3,4} (RPE%-RAE%) (RPE%-RAE%) (RPE%-RAE%) Comput.(SNR = 60 dB) 0.65 ; -81.81 16.35 ; 2.47 1.56 ; 0.08 Comput.(SNR = 33 dB) 14.20 ; -81.81 75.16 ; (*) 34.13 ; 2.43

Figure 4. Estimation of the air-gap thickness using a 5-frequency 2nd order polynomial forward model for a tc = 1.5 mm; tr = 1.5 mm configuration. a) simulated data (SNR = 33dB), b) experimental data (SNR = 33 dB)

The simulated test set is constituted by the configurations described in section 2.1., but with t taking 11 values linearly arranged within the 0 to 500 μm range. For each of these configurations, 1000 random noise trials are used. Regarding the experimental data, the test set is constituted by data relative to configurations featured by t ranging from 0 to 500 μm, and tc = 1.5 mm (which constitute the worst case for the estimation). For each considered configuration, each measurement was repeated 12 times (with sensor dismounting) so as to take uncertainty into account. Finally, in order to

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characterize the estimation results, we consider the relative accuracy error (RAE) and the relative precision error (RPE), defined in (8), where tˆ is the estimate of t, and where mean(.) and std(.) denote the mean value and the standard deviation, respectively.

§ tˆ − t · RAE % = mean ¨100. ¸ t ¹ ©

and

§ std (tˆ) · ¸ RPE % = mean ¨¨ 100 . mean (tˆ ) ¸¹ ©

(8)

The estimation of the distance between parts using 3, 4 and 5 excitation frequencies was implemented according to (7). Estimation errors obtained using simulated data featured by a 60 dB and a 33 dB signal to noise ratio (SNR) and experimental data of 33 dB SNR are gathered in Table 1. The estimation errors significantly decrease when using a 5-frequency forward modeling (down to the order of 1 % for a 60 dB SNR). However, the estimation method exhibits a lower accuracy when the SNR falls down to 33 dB (Table 1, Figure 4), due to the poor conditioning of the forward matrix (6). Furthermore, the estimation errors are increased when obtained from the experimental data, due to the imperfect agreement between experimental and simulated data relative to the same configurations.

3. Estimation method relying on an inverse behavioral model

3.1. Inverse behavioral model (IBM) In order to enhance the estimation performances, we propose a second estimation technique, based on an IBM. Here, we aim at exploiting the linear characteristics (4). We build such sets of characteristics from simulated data obtained for discrete values of tr, considering the same assembly configuration and frequency sets as in section 2.1. Then, using 5th-order polynomials, we extrapolate the values of the slopes a −f 1 of i

equations (4) for any tr value comprised in the considered rib thickness range:

a −f i1 (tr ) = k5, f i t r5 + k 4, f i tr4 + k3, f i t r3 + k 2, f i t r2 + k1, f i tr + k0, f i

(9)

Provided the coefficients {k0,fi , ... k5,fi}, it is possible to estimate the air gap as follows. For every linear curve (4) corresponding to a given rib thickness trl, the measured NIDfi corresponds to a til air gap abscissa which is a possible solution of the problem:

til = a −f i1 (trl ). NID f i with tr1 ≤ trl ≤ trL and l ∈ {1,2,..., L}

(10)

Among the solutions provided by the equations (10), only those corresponding to the actual rib thickness, denoted tr l , will be true and also equal to each other. As a act

consequence, tr l may be estimated as the one such that the equations (10) satisfy: act tˆrl act = t rlˆ

act

so that

( ) = min{std (t ), std (t

std tilˆ

act

i1

i2

),..., std (tiL )}

(11)

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Finally, the air gap is estimated at every fi according to (12):

1 tˆ = N

N

¦t i =1

ilˆact

(12)

3.2. Estimation results and comparison The simulated and experimental data which the IPFM was applied to in section 2.2 are now used to implement the IBM. The estimation results obtained using simulated as well as experimental data featured by tc = tr = 1.5 mm and SNR = 33 dB (that is the worst estimation case considered) are given in Figure 5. For the simulated data, the RPE and the RAE are about 9.45 % and -10.38 % respectively, while for the experimental data they are 6.60 % and -10.03 % respectively. Results from simulated and experimental data are thus in good agreement and exhibit both satisfactory precision and accuracy. Furthermore, Table 2 compares the precision and the accuracy of the IPFM and of the IBM based estimation methods, considering a 5-frequency approach. The estimation relying on the IBM appears to be significantly more precise than that relying on the IPFM, whatever the considered case. In particular, with the IBM, in the worst cases considered the RPE does not exceed 10 % when it reaches 50 % with the IPFM. With regards to the accuracy, the two methods performances are in the same order.

Figure 5. Estimation of the air-gap thickness using a IBM: a) simulated data with the SNR = 33 dB, b) experimental data. Assembly configurations : tc = 1.5 mm ; tr = 1.5 mm ; t ∈ {0, 50, 100, 150, ...500) in μm Table 2. RAE and RPE of the air layer thickness estimations obtained using the IPFM and the IBM and a 5frequency approach. Assembly configurations tc = 1.5 mm ; tr = 1.5 mm ; t ∈ {0, 50, 100, 150, ...500) in μm Data IBM using fi i∈ {1,2,3,4,5} IPFM using fi i∈ {1,2,3,4,5} (RPE% ; RAE%) (RPE% ; RAE%) Comput.(SNR = 60 dB) 1.24 ; 0.42 0.93 ; 0.36 Comput. (SNR = 33 dB) 28.02 ; -0.20 9.45 ; -10.38 Experim.(SNR=33 dB) 49.16 ; -19.21 6.60 ; -10.03 Assembly configurations tc = 1.5 mm ; tr = 3.5 mm ; t ∈ {0, 50, 100, 150, ...500) in μm Data IBM using fi i∈ {1,2,3,4,5} IPFM using fi i∈ {1,2,3,4,5} (RPE% ; RAE%) (RPE% ; RAE%) Comput.(SNR = 60 dB) 1.56 ; 0.08 0.06 ; -0.03 Comput.(SNR = 33 dB) 34.13 ; 2.43 2.84 ; 1.10

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4. Conclusions

An experimental study of the coupling between a cup core coil eddy current sensor and a layered conducting assembly (similar to some aeronautical wing assemblies) has been reported. The analysis of the universal impedance diagram of the sensor has shown that the normalized impedance distance could be used with a view to the eddy current NDE of the distance between the conductive parts. These results, which have been confirmed by finite elements simulation results, led us to propose behavioral models of the coupling between the eddy current sensor and the layered structure. Furthermore, two methods for the estimation of the thickness of the distance between parts have been proposed and implemented. On the one hand, the estimation relied on the inversion of a polynomial forward behavioral model (IPFM), and on the other hand, an inverse behavioral model (IBM) was used. As far as the actual problem of the NDE of the assembly of a coating on a wing rib is concerned, two unknowns are to be estimated: the air layer thickness and the rib thickness, which may vary from one position on the inspected structure to another. As a consequence a multi-frequency estimation approach is necessary. The overall performances of the IBM based estimation method have proved to be more precise and as accurate as those of the IPFM based method. Further works will focus on the optimisation of the used EC sensor so as to increase the SNR of the EC data, as well as considering the elaboration of more accurate learning data set, so as to reduce the accuracy error. Also, dedicated sensor configurations will be designed so as to be used on actual aeronautical assembly geometries.

References [1] Y. Le Diraison, P.-Y. Joubert, D. Placko, Characterization of subsurface defects in aeronautical riveted lap-joints using multi-frequency eddy current imaging, NDT&E international 42 (2009), 133–140. [2] M. Wrzuszczak, J. Wrzuszczak, Eddy current flaw detection with neural network applications, Measurement 38 (2005), 132-136. [3] L. S. Rosado, T. G. Santos, M. Piedade, P. M. Ramos, P. Vilaça, Advanced technique for non-destructive testing of friction stir welding of metals, Measurement, In Press, Corrected Proof, Available online 13 February 2010. [4] S.N. Vernon, The universal impedance diagram of the ferrite pot core eddy current transducer, IEEE trans magn 25(3):2639–45 (1999). [5] J. Pavo, S. Gyimothy, Adaptative inversion database for electromagnetic nondestructive evaluation, NDT & E International 40 (2007), 192–202. [6] P. Huanga, G. Zhanga, Z. Wub, J. Caia, Z. Zhou, Inspection of defects in conductive multi-layered structures by an eddy current scanning technique: simulation and experiments, NDT&E international 39 (2006), 578–584. [7] I.T. Renakos, T.P. Theodoulidis, S.M. Panas, T.D. Tsiboukis, Impedance inversion in eddy current testing of layered planar structures via neural networks, NDT&E international 30 (1997), 69-74. [8] Y. Le Bihan, Study on the Transformer Equivalent Circuit of Eddy Current Nondestructive Evaluation, NDT&E International 36 (2003), 297–302. [9] C.V. Dood C V, W.E. Deeds, Eddy-current multiple property measurements, International Advances in Nondestructive Testing 9 (1981), 317-333. [10] H. L. Libby, Introduction to electromagnetic nondestructive test methods, Wiley, New York, 1971. [11] P. Y. Joubert, Y. Le bihan, Eddy Current Data Fusion for the Enhancement of Defect Detection in Complex Metallic Structures, International Journal of Applied Electromagnetics and Mechanics 19 (2004), 647 – 651.

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Artificial Heart Valve Testing Using Electromagnetic Method Tatiana STRAPACOVA1, Klara CAPOVA, Ladislav JANOUSEK, Milan SMETANA Department of Electromagnetic and Biomedical Engineering, Faculty of Electrical Engineering, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovak Republic

Abstract. The paper focuses on non-destructive inspection of BjĘrk-Shiley Convexo Concave artificial mechanical heart valves. A new approach for the inspection based on sweep frequency eddy current testing is proposed. The standard self inductance pancake probe positioned in proximity of the valve drives the eddy currents and pick-ups the response signal. The frequency of exciting current is changed in a wide range. Numerical simulations are carried out to verify the usefulness of the proposed technique. The gained results presented in the paper show that there is a clear difference in the amplitude frequency spectrum of the response signal between the intact valve and the other with a single leg fracture of the outlet strut. Keywords. non-destructive inspection, eddy currents, sweep frequency, outlet strut fractures, BjĘrk- Shiley Convexo Concave prosthetic heart valve

Introduction A dysfunction of the heart valve is a common complication after a heart valve disease. When the symptoms became intolerable with normal human lifestyle, the malfunction heart valve is replaced by an artificial one. Artificial heart valves are engineered mechanical metallic devices or they are made from a biological tissue.

Figure 1. Typical design of the BSCC heart valve and the fracture of the outlet strut.

1

Corresponding Author: Tatiana Strapacova, Department of Electromagnetic and Biomedical Engineering, Faculty of Electrical Engineering, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovak Republic; E-mail: [email protected]

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One of the artificial mechanical heart valves is the BjĘrk-Shiley Convexo Concave (BSCC) valve, shown in Fig. 1, which was developed in order to improve the hemodynamic and to reduce the risk of thromboembolism. BSCC was used to replace the aortic valves or the mitral ones. The BSCC valves have a carbon occluder disc held in the place by two metallic struts. One of the two struts, the inlet one is integrated into the valve suture ring, while the outlet one is welded into the suture ring. The suture ring made of Teflon is sewn to the cardiac tissue to hold the valve in the place. Approximately 120 thousand patients have received the BSCC [1]; however, in number of cases (619 patients, [1]) a malfunction of the valve has occurred because of the outlet strut fractures. The main reason of the outlet strut fractures has not been determined yet. The process of cyclic slamming open and shut of the occluder disc during heart function subjects the valve to percussive impact stress, which can cause a fatigue failure. These failures have been observed at the outlet strut flange junction near or at the weld. The failure of both struts results in dislodgement of the occluder disc and embolization of the disc. A dual strut failure results in abrupt onset of dyspnea, loss of consciousness, or cardiovascular collapse due to embolization of the disc and acute severe valvular regurgitation. A patient with the dual strut fracture of aortic prosthesis dies in minutes, but those with strut fracture of mitral prosthesis may survive long enough to undergo the valve replacement. Several types of mechanical BSCC heart valve failures have been reported in literature [1]: 1. an outlet strut fracture (OSF), fracture of both legs of the outlet strut, the strut is completely separated from the flange, 2. a single leg fracture (SLF), fracture of one leg of the outlet strut, both ends grate against each other, 3. a single leg separation (SLS), fracture of one leg of the outlet strut, both ends of the fractured strut are separated as displayed in Fig. 1. Although the function of the valve in the cases 2, 3 can continue under these conditions, the stress concentration on the intact end of the welded strut is increased and it is not clear how long the other end of the strut can remain intact. The period of time between the first and the second fractures is highly variable [1]. Due to this fact there is a considerable interest, therefore, to develop methods for assessing the state of the valve in general condition of the outlet strut weld by minimally invasive nondestructive inspection method. Electromagnetic methods represent a good candidate [2], [3] for the inspection. Eddy current non-destructive testing is widely utilized in a variety of industrial applications. An eddy current probe scans over an inspected surface and the response signals are evaluated accordingly. However, the conditions of considered application do not allow such scanning. A new approach for the non-destructive inspection of BSCC using eddy current technique is therefore proposed in the paper. It is based on sweep frequency technique. Numerical simulations are carried out to evaluate the proposal and the gained results are presented and discussed in the study.

1. Numerical model Possibilities of the sweep frequency eddy current inspection of BSCC are investigated in the paper using numerical means. The commercially available software OPERA-3D based on finite element method is utilized for the purpose.

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Standard self-inductance pancake probe, shown in Fig. 2, is used for the inspection. Dimensions of the probe are set up according to the dimensions of heart valve. Dimensions of the catheter which would be used for encapsulations of the coil are considered as well. The probe is positioned 1 mm above the weld of the outer strut where a crack is considered to appear. Current density of the exciting signal is kept constant during the inspection at a value of J = 1 A/mm2, while its frequency is changed in a wide range starting from 10 kHz up to 500 kHz.

Figure 2. Dimensions of the pancake probe.

A complex model of the BSCC shown in Fig. 3 is developed. The dimensions and the electromagnetic properties of model are adjusted according to the dimensions and the material properties of real BSCC heart valve. The materials commonly used for the BSCC heart valve replacement are Stainless steels, Titanium alloys and Co-Cr alloys. The developed model considers the electromagnetic parameters of a Co-Cr alloy Hayness 25; the conductivity is adjusted to ı = 1.14·106 S/m and the relative permeability to ȝr = 1.

Figure 3. Dimensions of the BSCC heart valve model.

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A considered defect is localized at one end of the outlet strut, Fig.3. The defect is non-conductive, i.e. fatigue crack, and it represents the single leg fracture (SLF) of the BSCC. Dimensions, an orientation and a depth of the defect are adjusted according to real conditions that may appear in the outlet strut of BSCC heart valve. A width of the modelled defect is set to w = 0.1 mm and its depth d is varied from 0.1 up to 1.9 mm with a step of 0.2 mm in a direction of the leg diameter. The single leg separation (SLS) is not considered in this study as the attempt of inspection should be early alarm of fatigue crack development. The numerical calculations were run for the intact outlet strut (IOS) for comparison as well. The modelled system considers also real environmental conditions, i.e. the blood and the tissue of myocardium as it is shown in Fig. 4. Electromagnetic properties of the blood and the myocardium are adjusted according to their real values presented in Tab. 1. The myocardium tissue is positioned around suture ring and the blood is inside the BSCC heart valve. Table. 1. Properties of the myocardium tissue and the blood for different frequencies.

Figure 4. Model configuration of the cardiovascular system

Numerical simulations of the developed model are carried out to calculate the probe response signal. The finite element mesh of the simulated problem has approximately 3 million elements of two types, linear and quadratic ones. The following section presents the results.

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2. Numerical results The results of numerical simulations of the model introduced in the previous section are presented here. Figure 5 shows amplitude frequency spectrum of the probe response signal in absolute values for four cases. The curve denoted as IOS represents the sweep frequency response signal for the intact outlet strut. The other three dependences are the response signals for the single leg fracture (SLF) with different depth of the defect, i.e. 0.1 mm, 0.5 mm and 1.9 mm. Similar results for the IOS and the SLF with the defect depth of 1.9 mm but in relative values are shown in Fig. 6. The inductive component of the probe response signal is dominant and thus the phase frequency spectrum does not show almost any difference between the IOS and the SLF.

Figure 5. Amplitude frequency spectrum of the probe response signal in absolute values

Figure 6. Amplitude frequency spectrum of the probe response signal in relative values

It is evident from the presented results that there is a clear difference in the amplitude frequency spectrum between the IOS and the SLF. It should be noted that the difference is more notable when the depth of defect is increasing. Difference in the dependences between the IOS and the SLF is largest in a frequency range from 70 kHz up to 150 kHz.

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It can be concluded that the sweep frequency technique is very promising for the eddy current inspection of the BSCC outer strut. The technique helps to overcome one problem connected with the eddy current inspection concerning the given conditions. The scanning over an inspected surface is not needed.

Conclusion The paper proposed a new approach for a defect detection in BjĘrk-Shiley Convexo Concave artificial heart valve using sweep frequency eddy current technique. This method detects perturbations in eddy current flow due to a defect in the outlet strut in a wide frequency range. A model of the valve was developed and the proposed technique was verified using numerical simulations. Presented results clearly showed that there is a clear difference in the amplitude frequency spectrum between the intact outlet strut and the strut with a defect. Experimental measurements are going to be carried out to confirm the numerical results.

Acknowledgement This work was supported by the Slovak Research and Development Agency under the contract No. APVV-0194-07. This work was also supported by grant of the Slovak Grant Agency VEGA, project No. 1/0308/08. The authors express their thanks to Prof. R. Grimberg for lending the valve prototypes.

References [1] Paul Van Neer: The BjĘrk- Shiley valve: Detecting broken struts using standards diagnostic ultrasound instruments, MSc Thesis, 2005 [2] Chan Shiu C., Yue Li, Udpa Lalita, Udpa Satish S.: Electromagnetic techniques for detecting strut failures in artificial heart valve, Studies in Applied Electromagnetics and Mechanics Electromagnetic, Vol. 26, Nondestructive Evaluation, Ed. G. Dobmann, ISBN 1- 58603-594-0 [3] Grimberg R, Lalita Udpa, Adriana Savin, Schiu C. Chan, Rozina Steigmann, Satish S. Udpa : Noninvasive evaluation of Bjork-Shiley convexo concave prosthetic heart valves, NDT&E, Int.(2009), doi: 10.1016/j.ndtteint.2009.01.013

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Conceptual Design of an Industrial System for Automatic Radiogram Analysis Ryszard SIKORA, Tomasz CHADY, Piotr BANIUKIEWICZ, Marcin CARYK, Przemysław ŁOPATO, Lech NAPIERAŁA, Tomasz PIETRUSEWICZ and Grzegorz PSUJ Department of Electrical and Computer Engineering, Faculty of Electrical Engineering, West Pomeranian University of Technology, al. Piastów 17, 70-310 Szczecin, Poland

Abstract. In this work a conceptual design of an Intelligent System for Radiogram Analysis (ISAR) is presented. ISAR is a complete system, containing both hardware and software solutions, that aims to support radiologists in their work. On the hardware side, we have a PC station with digital radiography scanner. The software side consists of application, that supports variety of scanner standards and implements number of functions designed to augment human-based defect recognition. ISAR also evaluates welds quality and returns information about welding defects to the database. Classification of defects is based on fuzzy logic standards. In this paper, hardware integration and implemented functions are described. Keywords. Radiogram, Non-Destructive Inspection, IQI, image processing

Introduction Non-destructive techniques of radiography inspection are widely used for damage detection in ship, car and aircraft metal structures. Among many kinds of defects and damages, it is also possible to detect weld defects using of industrial radiography technique [1]. The process of welded joints quality assessment must be very fast and accurate. Furthermore, type, size and acceptance level must be also determined for any heterogeneity in weld. The aim of ISAR project (Intelligent System for Radiogram Analysis, in Polish: Inteligentny System Analizy Radiogramów) is a creation of an intelligent expert system of recognition and rating of welds defects. There are various systems for radiography inspection of welding joints, including automatic analysis [2 – 5]. The ISAR is dedicated for shipbuilding industry in Poland. Integration between software and hardware is an important part of a concept of ISAR. Our system is composed of many different elements, all of which have to interoperate with designed software. It contains many image processing, analysis and recognition modules, full list of which can be seen in Section 2.2. All components of our system, both hardware and software, are integrated via single computer program, being core of our system. Software modules are easily integrated due to certain programmistic regime: all functions are in separate C++ files and written with use of an uniform template. This ensures easy integrability, as those

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can be both copied line by line to source code of core application, or compiled and included as libraries.

1. Hardware The ISAR system requires hardware and software of highest quality, which allows one to obtain high-quality results. On the hardware side we have: a PC computer with 6core 2.8GHz processor, 24 GB DDR3 RAM and graphical card with CUDA support; iCR 3600 image plate scanner [6]; Rad-Icon Shad-o-Box 1024 x-ray image sensor; Eltec P3I3 frame grabber; any TWAIN-interface scanner. Each of these components needed a different approach when it came to integration with designed software. The image plate scanner iCR 3600 was integrated using dedicated iCR software. Our program calls certain iCR program to handle all technical issues and leave the result in a tiff file. This is then read from hard drive by our software, which is transparent from the user’s point of view. The Rad-Icon Shad-o-Box 1024 was integrated via software development kit provided by Eltec P3I3 frame grabber’s manufacturer. The TWAIN interface was implemented with use of a TWAIN Group’s documentation and include files [7]. Figure 1 presents hardware used by ISAR.

2. Software 2.1. Requirements of ISAR-software ISAR application is build of many self-contained functions written in C++ environment and integrated in one software solution to create complete intelligent system. All algorithms implemented in our software take advantage of parallel computing whenever it’s applicable. The application was build for Windows x64 platform. The independence of functions gives the possibility of applications of different image processing procedure for each radiogram separately. We can also test all functions in Matlab software before using them in ISAR complete system. In Section 2.2 a select set of ISAR-functions are presented. 2.2. Implemented functions The Software side consists of application, that supports variety of scanner standards and implements a number of functions designed to augment human-based defect recognition. Those can be separated into few groups, namely: linear and nonlinear filtering algorithms (preliminary image processing), thresholding algorithms, quality of

Figure 1. The view of the hardware used by ISAR.

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image evaluation, as well as some specialized functions, such as IQI search function (that automatically detects and removes image quality indicators according to the standard). After the preliminary processing the image is shown and ISAR decides on welds quality and returns information about welding defects to the data base. 2.2.1. Preliminary image processing Image processing plays an important role in detecting weld flaws in radiograms. The quality of the images are enhanced by linear and nonlinear filters. The ISAR software implements high pass and low pass convolution filters (in spatial and frequency domain, with changeable mask size), Gauss, Laplace, LoG, Kirsch, Sobel, Prewitt filters. Figure 5b in Section 2.2.2 shows the effect of high pass filtering. Our system is also able to perform morphological operations. In our system, a weighted median filters with definable mask shape are implemented. This type of filters may be used for noise removal (smaller mask size) or background image calculation (bigger mask size). In order to obtain background image or determine center and other regions of the weld - an approximation procedure was carried out. Each line of the weld profile is approximated using the following or similar formula (Figure 2):

§ § ( x − b) · 2 · ¸ + dx + e f ( x) = a ⋅ exp¨ − ¨ ¨ © c ¸¹ ¸ © ¹

(1)

where: a, …, e – approximation coefficients, x – normalized position, f(x) – approximated intensity of image. For minimalization of Root Mean Square Error MSE between signal and intensity approximation, multidimensional Rosenbrock optimization algorithm was used with equation (1). Exemplary results are shown in Figure 3. The image obtained by subtracting the approximated image from the original one is also presented. Higher

Figure 2. Approximation of weld profile.

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Figure 3. Results of X-ray weld image approximation.

contrast and visibility of defects can be observed. To normalize radiographic images of welded parts the authors propose the use of image normalization function according to histogram point Ibase. The gray level value Ibase is equal to a point for which histogram has maximum value or is calculated as a mean value on determined image area. The value Inew base corresponds to gray level value of welding part (background). The procedure of image normalization is shown on Figure 4. An important parameter describing the radiogram taken into analysis is the signalto-noise ratio. This parameter is also defined by the norm - EN-14784-1. According to this norm SNR is evaluated between background of radiographic image and useful signal which is, in most cases, the signal from the specimen. There are some restrictions on choosing those regions. Firstly, the size of ROI should be at least 20x55 pixels, which gives 1100 values. Moreover, selected ROIs have to be the best representatives of background and specimen – for example the most important part of the specimen should be used for calculating the SNR. Selected ROI is assumed to be series of 55 datasets (groups) containing 20 values each. For every group i, the mean

Figure 4. Image normalization procedure: a) histogram after moving Ibase to Inew base, b) algorithm.

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value Imean i is evaluated as well as standard deviation ıi. Values of ıi have to be corrected by coefficient following from statistical analysis of filtration obtained as a result of data grouping (2).

σ corr = 1.0179 ⋅ σ i i

(2)

Then, the final value of Imean is calculated as median value of all Imean i. In the same way, the final value of ı is evaluated. This value should be related to spatial resolution of digital radiogram. Thus, ı yields to:

σ SR = σ ⋅ ( SRmax / 88.6 )

(3)

Where SRmax stands for spatial resolution (in μm) measured perpendicularly and horizontally to scanning direction. Finally, the normalized SNR is evaluated as:

SNR =

I mean

σ SR

(4)

2.2.2. Thresholding Thresholding is an important step in almost every algorithm designed for image analysis, radiogram defect detection being no exception. In our software a variety of thresholding algorithms, both local and global, have been implemented. Among those: - Iterative thresholding – computes global threshold in iterative way. It’s starting threshold is located in the middle of image’s dynamic range. In each iteration new threshold is computed using the average of mean values of background and foreground found with previous threshold. Algorithm stops when difference between nth and n+1st threshold is sufficiently small [8]. - Otsu thresholding – computes global threshold by minimizing weighted sum of within-class variance of background and foreground [8]. - Niblack thresholding – computes local threshold according to local mean and local standard deviation over a specific window with use of following formula [9]:

T (i, j ) = m (i, j ) + k ⋅ σ (i, j )

(5)

- Sauvola thresholding – is an expansion of Niblack’s thresholding, uses modified formula [10]:

­ ª σ (i, j ) º ½ T (i, j ) = m(i, j ) + ®1 + k ⋅ « − 1» ¾ ¬ R ¼¿ ¯ Figure 5c shows the result of Sauvola thresholding.

(6)

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2.2.3. IQI detection IQIsn function detects how many wires from single IQI are visible on radiographic image according to CNR (Contrast to Noise Ratio) [11, 12]. First the background of part radiographic image containing IQI is generated. This is done by using a median filter with the longitudinal mask. Then the background is subtracted from input image, and the CNR is calculated for each wire. The number of visible wires depends on the minimum calculated value of CNR. Figure 6 shows an example of an image before and after the operation. Table 1 shows results for example image where function detected 5 wires.

Figure 5. Example of implemented function’s work: a) original image, b) results of high pass filtering, c) results of Sauvola thresholding.

Figure 6. IQI detection example: a) original image, b) after IQI detection preprocessing.

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Table 1. Results of IQI detection on image from Figure 6. Wire MidPos Thicknes[mm] CNR

1 76 0,4 12,2

2 195 0,32 10,52

3 310 0,25 7,17

4 421 0,2 6,79

5 531 0,16 1,99

3. Conclusions The conception of ISAR system is prepared to apply in industrial non-destructive testing. Presented functions do not encompass entire functionality of presented system, as it is freely expandable due to described programmistic approach. Final effect of ISAR project will be a complete intelligent system. Functions described in this text can effectively improve the quality of X-ray radiograms and assist in the extraction of information concerning defects in the weld.

Acknowledgments This work was supported by the Ministry of Education and Science, Poland, under grant N R01 0037 06 (2009–2012).

References [1] Alaknanda, R.S. Anand, Pradeep Kumar, Flaw detection in radiographic weld images using morphological approach, NDT&E International 39 (2006), 29–33. [2] Dong Du, Guo-rui Cai, Yuan Tian, Run-shi Hou, Li Wang, Automatic Inspection of Weld Defects with X-Ray Real-Time Imaging, Lecture Notes in Control and Information Sciences, Vol. 362/2007, 359366 (2007) [3] R. D. Bowman, B. A. Bennett, M. E. Stevenson, Radiographic inspection in failure investigations, Journal of Failure Analysis and Prevention. Vol. 3, Number 3, 73-77 [4] GE Sensing & Inspection Technologies. Inspection Technologies Productivity through inspection solutions. Advanced nondestructive imaging, http://www.ge-mcs.com/download/it-common/GEIT10012EN ndt-brochure.pdf [5] T. Warren Liao, Yueming Li, An automated radiograp.hic NDT. system for weld tnspection:. Part IIFlaw detection,.NDT&E International, Vol. 31, No. 3, pp. 183-192 (1998). [6] http://www.icrcompany.com/Computed-Radiography/3600.html [7] http://www.twain.org/ [8] M. Sezgin, B. Sankur, Survey over image thresholding techniques and quantitative performance evaluation, Journal of Electronic Imaging 13(1), 146–165 (January 2004). [9] Naveed Bin Rais , M. Shehzad Hanif and Imtiaz A. Taj, Adaptive Thresholding Technique for Document Image Analysis, 8th IEEE International Multitopic Conference (INMIC), Lahore, Pakistan, December, 2004 [10] J. Sauvola, M. Pietikainen, Adaptive Document Image Binarization, Pattern Recognition, vol. 33, 110.2, pp. 225- 236, 2000 [11] U. Ewert, U. Zscherpel, K. Bavendiek, Strategies for Film Replacement in Radiography - a comparative study, IV Conferencia Panamericana de END Buenos Aires – Octubre 2007. [12] U. Ewert, U. Zscherpel, C. Bellon, Gerd-Rüdiger Jaenisch, J. Beckmann, M. Jechow, Flaw Size Dependent Contrast Reduction and Additional Unsharpness by Scattered Radiation in Radiography Film and Digital Detectors in Comparison, 17th World Conference on Nondestructive Testing, 25-28 Oct 2008, Shanghai, China.

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Quantification of Sigma Phase Precipitation by Magnetic Non Destructive Testing João M. A. REBELLOa,1, Rodrigo SACRAMENTOa, Maria C. L. AREIZAa, K. SANTOS DE ASSISa a Non-destructive Testing, Corrosion and Welding Laboratory – Department of Metallurgical and Materials Engineering COPPE/UFRJ – Federal University of Rio de Janeiro – Rio de Janeiro/RJ - Brazil Abstract. Duplex stainless steels (DSS) are two-phase materials the microstructure of which consists of grains of ferrite (į) and austenite (Ȗ). DSS exhibit a combination of attractive properties: strength, toughness and ductility, stress corrosion cracking resistance and low cost, when compared to the conventional stainless steel. DSS are increasingly used in the oil refinery industry, mainly due to their economical combination of strength and corrosion resistance even in H2S containing environments. However, DSS attain these attractive properties after a controlled solution heat treatment carried out during manufacture, leading to an equal and balanced proportion of the volume fractions of į and Ȗ phases. Regarding the DSS magnetic properties, it is known that į is ferromagnetic and Ȗ is paramagnetic. Any further heat treatment carried out after manufacture, welding operation for example, will change the original 50% į and Ȗ base metal phase proportion. So the weld heat affected zone microstructure, where temperatures reach values between 300°C and 1000°C give origin to non-balanced į and Ȗ phases. Besides, exposition to these high temperatures may lead to precipitation of a deleterious phase, named sigma (ı), and when this occurs the material becomes brittle and its corrosion resistance to H2S is severely impaired. In the present work, the degradation of the material was intentionally obtained by thermally treating DSS specimens, at temperatures ranging from 750°C up to 800°C, after solution heat treatment at 1200°C giving rise to different ı phase contents. These specimens were analyzed by optical microscopic techniques to determine the volumetric fraction of the ı phase. The results showed that samples heat treated in this way, exhibited volumetric fraction of ı phase ranging from zero to 15.63%. In parallel, eddy currents (EC) testing and swept frequency analyses were employed to detect ı phase. A probe consisting of one coil, with cylindrical geometry, 1000 wire turns and a ferrite core of 10mm diameter was designed for the implementation of this technique. The probe exhibited its higher sensitivity at low frequencies around 4 kHz and its inductance was 22.42 mH. The results showed that magnetic testing is a reliable technique to detect and quantify the ı phase in DSS. Keywords. Eddy Current, duplex stainless steel, sigma phase

Introduction DSS present a good combination of mechanical properties and high corrosion resistance due to the presence of two phases (į and Ȗ) in their microstructure [1], and 1

Metallurgy and Materials Dept.Federal University of Rio de Janeiro. COPPE/EE/UFRJ. PO BOX 68505 CEP 21941-972. Rio de Janeiro, RJ BRAZIL E-mail: [email protected]

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are widely used in the marine and petrochemical industries. Such microstructure consisting of two different phases, γ and δ, with very different physical properties (austenite presents high electric conductivity and low magnetic permeability and ferrite presents low electric conductivity and high magnetic permeability) renders the inspection through non-destructive testing techniques, difficult. DSS best properties are obtained in solution with approximately equal proportions of phases į and Ȗ [2,3]. Welding operation may lead to microstructural changes of the base metal and heat affected zone (HAZ), changing the balance of į and Ȗ phases and/or causing the precipitation of deleterious phases due to steel exposition to temperatures ranging from 300º C to 1000º C. The most harmful of the deleterious phases that can be originated in the material microstructure is ı phase, because it presents higher volumetric fraction than others and its precipitation causes chromium depletion in the adjacent regions, impairing mechanical and corrosion properties of the material. The presence of ı phase causes a change of the electromagnetic properties of DSS. Ferrite is ferromagnetic while austenite and σ phase are paramagnetic. Thus an increase in σ phase percent and the resulting decrease in δ phase volumetric fraction render the material behavior more paramagnetic. This characteristic makes the EC technique an interesting non destructive tool for the detection of material degradation caused by an increase in ı phase percent.

1. Theoretical review 1.1. Duplex Stainless Steels Commercial DSS present chromium content, which is an element that favors the formation of į phase, varying from 17% to 30%, nickel content, which is an element that favors the formation of Ȗ phase, varying from 3% to 13% and molybdenum content, which is also a ferrite former element, varying from 2% to 4%, while manganese and silicon are used for alloy deoxidation [4]. Due to their good combination of properties, DSS have been increasingly used in the chemical, power generation and on off-shore industries [1]. In the off-shore industry, DSS are used both, in oil and gas production and processing and transportation, in the production of water and water systems at the sea, in the manufacture of subsea umbilical and submerged components without cathodic protection, among others [5]. These steels have also been used successfully in the petroleum refining industry in pipes, plates, pressure vessels and heat exchangers in corrosive environments containing H2S and water with chloride [6,7]. Maehara [9] reported the relationship between the toughness at room temperature and the volumetric fraction of σ phase. A decrease in the impact energy absorbed by the material even for a small increase in the σ phase volume fraction was observed. These measurements were made at room temperature.

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1.2. Magnetic properties As already said, the two phases present in DSS microstructure show very different magnetic properties. Austenite, Ȗ phase presents high electric conductivity and low magnetic permeability and į phase presents low electric conductivity and high magnetic permeability [3]. Besides, į phase shows a ferromagnetic behavior while Ȗ phase shows a paramagnetic behavior [10, 11]. When both phases are in equal proportion or with a higher į phase percent DSS show a ferromagnetic behavior. The presence of σ phase causes a change in the balance between į and Ȗ, and consequently the magnetic properties of the steel also change. Some authors mention ı phase as non-magnetic [8, 10, 11, 12], so an increase in its volumetric fraction causes a decrease in the ferromagnetic behavior of the material. Some papers [12,13] show that magnetic saturation of DSS is proportional to δ volumetric fraction, and thus its decrease due to an increase in ı phase causes a change of the magnetic properties of the material. Mészáros [12] obtained magnetization curves for DSS with different į phase percents using the vibrating sampler magnometer (VSM) technique. From those magnetization curves, a quantitative correlation between the values of magnetization in the saturation region of the curves and į phase percent in different samples was obtained. It was observed a good correlation between saturation induction and ferrite content obtained with VSM and į phase content [12]. The magnetic properties of phases į and Ȗ are well described in literature, however the magnetic properties of ı phase, and its influence on the properties of DSS need to be further studied. The only mention founded in the literature about this matter was from Todorov [11], who showed that a qualitatively correlation exists between ı phase percent and conventional EC parameters. 2. Materials and methodology 2.1. Materials - Eight DSS samples, specification UNS 31803, with length 50 mm, width 32 mm and thickness 4 mm were used. Table 1 shows the correspondingly chemical composition. Table 1. Chemical Composition of DSS (UNS S31803)

Element UNS S 31803 (%wt)

C

Si

Mn

Ni

Mo

Cr

0.034

0.283

1.78

5.58

2.87

22.02

- Heat treatment furnace with maximum temperature of 1300ºC; - Optical microscope (OM), ZEISS Axio Imager, with working station and software for image acquisition, processing and analysis (Axio Vision and Image Pro);

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- Scanning electron microscope (SEM) of 30 kV with low vacuum capacity, ZEISS EMA-25, equipped with Energy Dispersive Spectroscopy detection system (EDS), Oxford Inca Synergy 350 integrated system; - EC equipment, Olympus Omniscan MX; - Impedance analyzer HP 4295A; - EC probe customized for material characterization; 2.2. Methodology •

Heat treatments

Initially the eight samples were submitted to a preliminary solution heat treatment aiming at obtaining a percent balance of approximately 50% of both δ and γ phases. The solution heat treatment was conducted at 1120º C during one hour, followed by water quenching. Six samples received additional aging heat treatments which introduced different amounts of σ phase volumetric fractions. Table 2 shows the correlation between the different heat treatments and the percentage of each phase obtained in all the samples used in this study. Table 2. Correlation between samples, heat treatments and phase content. Austenite Ferrite Time of Sample Temperature heat of heat treatment treatment 1 1120º C 1h 44.56% 55.44% 2 1120º C 1h 44.51% 55.49% 3 800º C ½h 43.38% 55.92% 4 800º C ½h 43.56% 55.69% 5 800º C 1h 49.10% 42.46% 6 800º C 1h 45.76% 45.88% 7 750º C 2h 47.25% 37.12% 8 750º C 2h 47.28% 37.64%

•

Sigma phase

0% 0% 0.70% 0.75% 8.44% 8.36% 15.63% 15.08%

Metallographic analysis

A small portion (15 mm long, 5 mm wide and 4 mm thick) was removed from each sample so that they could be examined through SEM, EDS and OM. For this purpose the conventional method of mechanical polishing were used followed by an electrolytic chemical attack in 30% solution of NaOH – 3V over a time varying from 5 to 60 seconds in order to reveal their microstructures. ASTM A 923 standard was followed in these procedures [14]. After preparation the samples were examined by OM and 30 images were randomly captured in different regions of the transversal section of each sample. Those images were used for counting the phases volumetric fraction in the microstructure as specified by ASTM E1245-03 [15]. Besides OM, SEM images were obtained and EDS analysis were made.

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• Probe simulation In this study the simplest geometrical shape for probe design, e.g, a cylindrical metallic bobbin core was used, and the mathematical model adopted was an azimuthal approximation. Figure 1 shows the principal regions of the model: (A) a ferritic core, (B) a bobbin with N turns, and (C) the air. The vertical axis corresponds to the symmetrical axis, and the horizontal axis is the parameter r, so, all of the components are in the rz plane. An alternated induced current is applied on B region in the normal direction to the rz plane. The corresponding generated magnetic field is more intense in the core region. (Fig. 1, right). The mathematical calculation of the induced current follows equation 1, which is the time-harmonic formulation (Vloop) in a quasi-static operational condition. It contains the Curl of the magnetic vector potential. In this equation ω is the angular frequency, σ the conductivity, ȝ the permeability, ε the permittivity, and Vloop the voltage applied to the coil. Outside the coil and core, σ is set to zero.

& & & σ.Vloop ( jωσ − ω2ε ) Aϕ + ∇ × (μ −1∇ × Aϕ ) = Jϕe = 2πr

(1)

r(mm)

Core

Coil

Figure 1. Azimutal model for EC simulations.

The current induced, I, is calculated from the current density,

&e & .ds = I

³J

J ϕe (Eq. 2) (2)

S

The model has to define the boundary condition for the outer border, called magnetic insulation. This implies that the magnetic vector potential is zero at the boundary, corresponding to a zero magnetic flux (Eq. 3). Other boundary condition is the symmetry of the magnetic potential vector with respect to the z axis. Finally, the magnetic potential must be continuous (Eq. 4) inside A, B and C regions, e.g., the core, the copper wires, and surrounding air.

n× H = 0

(3)

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•

n × ( H1 − H 2 ) = 0 Probe construction

(4)

A probe consisting of one coil, with cylindrical geometry, 1000 wire turns and a metallic core of 10 mm diameter was designed for the implementation of this technique. The internal radius was 5 mm and the external radius 5 mm. The material of the core was ANSI 1045 type. Swept frequency measurement was made to detect the region of frequencies with high sensitivity. The probe exhibited its higher sensitivity at low frequencies, around 4 kHz and its inductance was 22.42 mH, figure 2. But, regarding the second derivative curve, there is also a point at 2kHz where a good option for high sensitivity measurements is possible, as another alternative to be used.

Figure 2. Swept frequency measurement, probe at air.

•

Measurement of magnetic field attenuation

The magnetic field generated by the coil is attenuated when it spreads through the ferrous material. This magnetic field attenuation was measured in samples of DSS with 4 mm of thickness and (4x4) mm of area. BRelative was the parameter used for the quantitative evaluation of the interaction of the magnetic field with the material, it is defined by equation 5, where BAir is the magnetic flux density measured at air and BMaterial is the magnetic flux density measured in contact with the material. The schematic representation of the setup is shown in figure 3. The measurements of magnetic flux density were made with a FW Bell Gaussmeter (Model 6010) and the current source was the Agilent 33250A. The current of the probe was setup at 10 Vpp and 40 Hz.

BRe lative( Air ) =

(BAir − BMaterial ) B Air

(5)

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Figure 3. Schematic setup for the measurements of magnetic attenuation. (A) Direct measurement of the magnetic field generated by the bobbin; (B) Magnetic measurements at the backside of the sample.

•

Measurement of conventional EC

In this test, the EC signal produced at a point distant from the conductive samples (signal in air, Fig. 3A) was taken as reference and then, the probe was brought in contact to each of the eight samples surface (Fig. 3B). The amplitude and phase angle of those signals were measured. In order to statistically improve the results 30 measurements were taken for each sample and at the end, the average was calculated obtaining the final value for amplitude and phase of each sample. Then, the values obtained during the EC tests were correlated with the percentage of σ phase in each sample. •

Measurement of swept-frequency

Swept frequency measurements were made in a range of 40Hz until 30kHz. Two different electrical parameters were analyzed: impedance and inductance, using the same setup described for EC. In equation 6, a parameter LRelative was defined, in order to compare the value of the inductance at one specific frequency (2 and 4 kHz). Similar parameter was defined for the electrical impedance (ZRelative).

LRe lative ( Air ) =

3.

(LAir − LMaterial ) LAir

Z Re lative ( Air ) =

(Z Air − Z Material ) Z Air

(6)

Results and discussion

3.1. Metallographic analysis Figure 4 shows the SEM image of sample 1, where phases į and Ȗ in approximately the same proportion can be observed in the DSS microstructure.

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Figure 4. SEM image of sample 1.

Figure 5 shows a SEM micrograph of Sample 6 (S6) and its respective EDS spectra. In this figure, quantitative EDS analyses were performed in three points, each one representing one of the three focused phases. Point 1 represents į phase, demonstrated in the spectrum by the presence of chromium, smaller presence of nickel and presence of molybdenum. Point 2 represents Ȗ phase, demonstrated by higher nickel and smaller chromium presence when compared to point 1. Point 3 represents σ phase, demonstrated by chromium presence similar to point, higher presence of molybdenum and smaller nickel presence.

Figure 5. SEM image indicating the Sample 6 points where EDS analyses were conducted and their respective spectra.

3.2. Conventional EC Figure 6A shows the lift-off signals obtained in the EC test for samples 2, 4, 6 and 8. In this figure the signals are shown in the impedance plane, characteristic of EC technique. The same signals of the impedance plane are presented through the

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components of the plane (resistive or inductive) as shown in figure 6B. A frequency of 4 kHz with a gain of 32dB and a 4V drive were used to obtain those results. Figure 6 shows that EC technique was able to differentiate the four samples tested in this study, which received different heat treatments and thus exhibited different volumetric fraction of σ phase. It is worth mentioning that the inductive component (XL , Fig. 7B) of the EC test was the most sensitive to detect small variations in σ phase contents, compared to the resistive component.

Figure 6. Lift-off signals obtained for the four samples through the EC technique with frequency of 4 kHz. (A) Impedance plane; (B) Resistive and inductive components.

3.2. Swept-Frequency Swept frequency measurements were made in a range from up to 30 kHz. Two different electrical parameters were analyzed: impedance and inductance. Figure 7 shows the good differentiation of the samples with different volumetric fraction of σ phase, for frequencies up to 9kHz.

Figure 7. Sweep frequency measurements of inductance.

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Figure 8 shows the values of the relative parameters, LRelative and ZRelative (Eq. 6) for the two best operation frequencies, as indicated in figure 2. At 2 kHz, 28% of signal difference was obtained between a sample without σ phase and the samples 7 and 8, 15.63% and 15.08% of σ phase, respectively. A higher sensitivity was observed in the measurement with small σ phase content. For this case, we observed a change of almost 6% in the electrical parameters reported.

Figure 8. Attenuation of electrical parameters with the influence of σ phase (Equation 6)

Small contents of σ phase are enough to change the electrical impedance and inductance. This behavior is not caused by an increase in δ phase of the material, but by the presence of the deleterious σ phase. Figure 9 shows the attenuation produced by σ phase (Eq. 5), and this result was obtained after 10 measurements for each sample and the standard deviation was less than 2%. The attenuation of magnetic field is strongly dependant on volumetric fraction of σ phase. This is in agreement with the previous results of conventional EC and swept frequency. The absolute value of magnetic field attenuation, observed in figure 9, could be a function of the thickness sample, and this implies that for 4 mm we observe 10 % of difference of attenuation. But for a thicker sample a greater absorption of magnetic field by the material could be observed

Figure 9. Measurements of BRelative (Equation 5) as function of σ phase content.

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4.

Conclusions

-

Sigma phase is responsible for the differences in the magnetic attenuation within DSS; Swept frequency measurements have shown to be an efficient tool for the characterization of DSS in the range of 0.70% to 15.63% of volume fraction of sigma phase; The eddy current technique has proved to be equally able to detect and quantify sigma phase in DSS samples; Low frequencies are more suitable for reliable material characterizations when using 2kHz and 4kHz probe frequency; Differences of 28.9% and 33.7% in the signal for the inductance (L) and impedance (Z) parameters respectively were observed for the samples containing sigma phase in relation to air.

-

-

References [1] V. CHIAVERINI, Aços e Ferros Fundidos, São Paulo, 2005. [2] H. Sieurin, Sigma phase precipitation in duplex stainless steel 2205, Materials Science and Engineering A444 (2006), 271-276. [3] K.S. de Assis, Caracterização por Correntes Parasitas da Degradação Microestrutural de Aços Duplex, 10ª COTEQ (2009). [4] C.H. Shek, Review of Temperature Indicators and the Use of Duplex Stainless Steels for Life Assessment, Materials Science & Engineering 19 (1996), 153 – 200. [5] M. Tystad, Application of Duplex Stainless Steel in the Off-Shore Industry, Stainless Steel World – KCI Publishing (1997). [6] API – American Petroleum Institute, Use of Duplex Stainless Steels in the Oil Refining Industry, API Technical Report 938-C (2005). [7] T.H. Chen, The effect of High Temperature Exposure on the Microstructural Stability and Toughness Property in a 2205 Duplex Stainless Steel, Materials Science & Engineering A338 (2002), 259 – 270. [8] C.M. Souza Jr., The ı Phase Formation in Annealed UNS S31803 Duplex Stainless Steel: Texture Aspects, Materials Characterization 59 (2007), pp. 1301 – 1306. [9] Y. Maehara, Precipitation of ı Phase in a 25Cr-7Ni-3Mo Duplex Phase Stainless Steel, Tetsu-to-Hagané 67 (1981). [10] N. Sathirachinda, Depletion effects at phase boundaries in 2205 duplex stainless steel characterized with SKPFM and TEM/EDS, Corrosion Science 51 (2009), 1850 – 1860. [11] E.I. Todorov, Correlation between NDT Measurements and Sigma Phase Contents in Duplex Stainless Steels, Review of Quantitative Nondestructive Evaluation 28 (2009), 1259 – 1266. [12] I. Mészáros, Magnetic Characterization of Duplex Stainless Steel, Physica B 372 (2006), 181 – 184. [13] I. Mészáros, Complex Magnetic and Microstructural Investigation of Duplex Stainless Steel, NDT & E International 38 (2005), 517 – 521. [14] ASTM – American Society for Testing and Materials, Standard Test Methods for Detecting Detrimental Intermetallic Phase in Duplex Austenitic/Ferritic Stainless Steels, ASTM A 923 – 03 (2003). [15] ASTM – American Society for Testing and Materials, Standard Practice for Determining the Inclusion or Second Phase Constituent Content of Metals by Automatic Image Analysis, ASTM E 1245 – 03 (2006).

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Nondestructive Characterization of Neutron Induced Embrittlement in Nuclear Pressure Vessel Steel Microstructure by using Electromagnetic Testing I. ALTPETER1, G. DOBMANN, G. HÜBSCHEN, M. KOPP and R. TSCHUNCKY Fraunhofer-Institut für Zerstörungsfreie Prüfverfahren, Saarbrücken, Germany

Abstract. Using nuclear power for energy generation, pressure vessel walls are exposed to neutron fluences of different levels depending on the distance to the core. Hence materials undergo a change of microstructure in terms of embrittlement, to be measured as toughness reduction and shift of the Ductile–toBrittle Transition Temperature (DBTT) to higher temperatures. Normally plant safety concerning this change in microstructure is ensured by destructive testing of surveillance samples. These are standard tensile and Charpy specimens which consist of exactly the same material as the pressure vessel and its weldments, being exposed to accelerated irradiation rates within special irradiation channels allowing a pronounced ageing. During revision downtime of the plant these samples are tested destructively in standard tensile tests at 423 K and 548 K respectively or by measuring the impact energy as a function of temperature in Charpy tests to determine the shift of DBTT. It is demonstrated that electromagnetic parameters allow characterizing the changes in the microstructure generated through neutron irradiation. After a defined calibration process a quantitative characterization of the embrittlement especially in terms of DBTT is possible. This has been demonstrated for reactor pressure vessel steels according to western design as well as to eastern specifications. As testing methods 3MA (Micromagnetic, Multiparameter, Microstructure and stress Analysis) and dynamic magnetostriction using EMATs (ElectroMagnetic Acoustic Transducers) have been applied. Keywords. EMAT, 3MA, neutron embrittlement, pressure vessel

Introduction Nondestructive material characterization techniques have traditionally been employed to detect, classify and size defects in materials. However in the last two decades a significant amount of effort has been invested to develop NDT techniques which can reliably characterize materials in terms of properties describing the fitness for use. In the case of power plant components, such as pressure vessels and pipes, the fitness for use under mechanical loads is characterized in terms of the determination of mechanical properties such as mechanical hardness, yield and tensile strength, toughness, shift of Ductile-to-Brittle Transition Temperature (DBTT), fatigue strength. 1

Corresponding Author.

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With the exception of hardness tests which are weakly invasive, all of these parameters can be determined within surveillance programs by using destructive tests on special standardized samples (Charpy specimens). The specimens are exposed in special radiation chambers near the core of the nuclear power plant (NPP) to a higher neutron flow than at the surface of the pressure vessel wall. From time to time these specimens are removed from the chambers and used for destructive tests. The number of the Charpy specimens is limited and in the future it will be very important that nondestructive methods are available to determine the mechanical material parameters on these Charpy specimens. Furthermore in situ characterization of the reactor pressure vessel inner wall through the cladding is of interest additionally to the measurements on Charpy specimens. To solve this task a combination testing method based on 3MA (Micromagnetic, Multiparameter, Microstructure and stress Analysis) [1] and dynamic magnetostriction by using an EMAT (ElectroMagnetic Acoustic Transducer) [2] was developed. Electromagnetic methods have a high potential to characterize neutron induced microstructure states.

1. Assessment of the Embrittlement In addition to the mechanical properties, the embrittlement phenomenon also influences the magnetic properties. Even the smallest changes in the materials state can affect the magnetic domain structure. Micromagnetic test methods have a high potential to detect the change of microstructure defects e.g. precipitations since they sensitively react to changes of the domain wall (which separate the magnetic domains) configuration. Therefore electromagnetic procedures could potentially be used to assess the material embrittlement. The neutron induced embrittlement results in microstructure changes. These microstructure changes lead to the generation of vacancies and precipitations of Cu-rich coherent particles (radius: 1-1.5 nm). This results in an increase of yield strength and tensile strength, a decrease of Charpy energy upper shelf value and an increase of the shift of DBTT by 41 joule (ǻT41). The potential of electromagnetic testing methods for detection of microstructure states is based on the analogy between the interaction of dislocation with microstructure states and of Bloch-walls with microstructure states. Similar to the movements of dislocations under mechanical load Bloch-walls move under magnetization. Therefore an analogy exists between mechanical technological values (e.g. hardness values) and magnetic values. So the interaction between dislocations and copper particles leads to an increase of mechanical hardness and the interaction of the copper particles and Bloch-walls leads to an increase of magnetic hardness. The potential of electromagnetic testing methods for the detection of copper precipitations was demonstrated on the Cu-rich pressure vessel and piping steel 15 NiCuMoNb 5 (1.65 weight % Cu) [3]. The analogy between mechanical and magnetic hardness is shown in the behavior of both hardness values as function of simulated service time at 673 K (see Figure 1). The hardness maximum is in the order of a service time of 1000 h.

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Simulated service time at 673 K [h]



Figure 1. Magnetic coercivity compared with the mechanical hardness for the detection of copper precipitations in Cu-rich pressure vessel and piping steel 15 NiCuMoNb 5 (1.65 weight % Cu). Mechanical hardness: circles, magnetic hardness: squares.

Since the dynamic magnetostriction using an EMAT is sensitive for lattice defects it was assumed that a magnetostrictively excited standing wave in the pressure vessel wall also reflects the neutron embrittlement and first experiments were performed with a special designed magnetostrictive transducer at Charpy specimens in the hot cell in order to principally demonstrate the potential. Using several electromagnetic measurements at the same time, a variety of measuring quantities is derived for each measurement cycle. When combined, they achieve the desired result (e.g. material property) more efficiently compared to individual measurement. By using a calibration function or pattern recognition the desired quantity of an unknown set of samples investigated by that method can be detected nondestructively.

2. NDT Characterization of the Neutron Irradiation Induced Embrittlement Depending on the specific design of a pressure vessel – which varies in different countries – the pressure vessel material in nuclear power plants is exposed to neutron fluences in the range between 5.6×1018 n/cm2 and 86.0×1018 n/cm2. In order to characterize the neutron irradiation-induced embrittlement, Charpy specimens exposed to neutron fluence in the above mentioned range have been investigated in a hot cell at AREVA NP GmbH whereby only the 3MA and EMAT sensors were arranged within the hot cell and the electronic equipments (3MA and EMAT device) was outside (see Figure 2). These Charpy specimens (base material and weldments) of eastern and western design have been provided by AREVA NP GmbH and Research Centre Dresden-Rossendorf e.V. (see Table 1)[4].

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325

3MA testing device

EMAT testing device

Neutron irradiated Charpy-specimens of reactor pressure vessel materials of western and eastern design Base material and weldments

 Figure 2. Used equipment for electromagnetic measurements in the hot cell

Sample set of neutron irradiated base material Material

Short term Neutronfluence [n/cm²]

Range ΔT41 [K]

22 NiMoCr 3 7

P7

0 – 40.3 x 1018

0 - 32

20 MnMoNi 5 5

P141

0 – 10.7 x 1018

0-9

22 NiMoCr 3 7

P147

0 – 43.8 x 1018

0 - 23

ASTM A508 C1.3 (22 NiMoCr 3 7)

JFL

0 – 86.0 x 1018

0 - 78

ASTM A533B C1.1

JRQ

0 – 98.0 x 1018

0 - 221

(20 MnMoNi 5 5 )

Sample set of neutron irradiated weldments Material

Short term Neutronfluence [n/cm²]

Range ΔT41 [K]

S3NiMo3-UP

P16

0 – 11.7 x 1018

0 - 67

S3NiMo1-UP

P141

0 – 49.7 x 1018

0 - 38

S3NiMo1

P140

0 – 10.4 x 1018

0 - 21

Table 1. Overview of the set of neutron induced Charpy specimens (base material and weldments)

Furthermore Charpy tests were carried out for determination of the shift of DBTT (reference values).

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Based on the data base consisting of EMAT and 3MA measuring quantities and the reference values pattern recognition and regression functions for calibration were developed. One part of each Charpy specimen set was used to calibrate and the other part – independently selected – was taken to test the model. The pattern recognition algorithm, mentioned above, was used to obtain approximation values of the shift of DBTT, which is a measure of the embrittlement (see Figure 3 and Figure 4).

 Figure 3. Predicted shift of the DBTT for RPV-base material versus shift of DBTT determined by the Charpy test

 Figure 4. Predicted shift of the DBTT for RPV-weldments versus shift of DBTT determined by the Charpy test

It was demonstrated that the prediction of the shift of the DBTT can be performed due to the micro-magnetic procedure. For the validation samples (base material) a correlation coefficient of R²=0.98 and a RMSE (root mean square error) of 10.13 K was obtained. In the case of the weldments the correlation coefficient was R²=0.99 and the RMSE value was 3.18 K.

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With regard to in situ measurements on the reactor pressure vessel inner wall through the austenitic cladding test measurements with 3MA and the dynamic magnetostriction-technique using an EMAT were carried out at a ferritic test piece with 8 mm thick austenitic cladding. In order to ensure deep penetration of the electromagnetic fields, low-frequency EMATs (” 40 kHz) were applied, and hence it was possible to characterize the material condition in the ferritic base material directly below the austenitic cladding from the clad side. Figure 5 shows the principle of such an inspection method [5] which up to now is not yet realized for inservice inspection.

 Figure 5. Principle of the magnetostrictive excitation of a standing wave in thickness direction of the pressure vessel wall by using an EMAT

The possibility of exciting and receiving ultrasonic waves in the ferritic base material through the cladding was documented by using HF-coil-configurations on clad test pieces by superimposing magnetic fields excited by u-shaped electromagnets. Values of signal-to-noise ratio of 23 dB were obtained on a ferritic test object with a wall thickness of 30 mm and with an austenitic cladding thickness of 8 mm. The magnetizing field strength was 260 A/cm and the selected frequency of the EMAT was 40 kHz.

8 mm cladding

8 mm lift-off

Figure 6. Ultrasound signals by an excitation on the austenitic clad side (left); Ultrasound signals by an excitation on the side without cladding with 8 mm lift-off (right)

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In a second experiment it was demonstrated that ultrasonic signals can still be produced even with a coil lift-off of 8 mm which was achieved by using an 8 mm thick PVC plate. The obtained EMAT-ultrasound echo signals are presented in Figure 6. Comparing the two acoustic signals it is obvious that the cladding is influencing the excitation of the magnetostrictively generated ultrasonic wave mainly by lift-off and not by eddy-current damping. Furthermore it also was shown that magnetic Barkhausen noise signals can also be received through the austenitic cladding with a good signal to noise ratio (Figure 7). It was demonstrated that the δ-ferrite changes in the cladding as well as a butt weld beneath the cladding do not disturb the ultrasonic amplitude very much (Figure 8).

Figure 7. Barkhausen noise profile curve measured on a ferritic testing sample through the 8 mm austenitic cladding

Figure 8. Variation of the ultrasonic signal amplitude along a butt weld beneath the cladding

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Therefore the non-destructive detection of the neutron irradiation by using 3MA techniques and the dynamic magnetostriction using an EMAT in a combination should be realized by developing an optimized transducer in the near future. The presence of the austenitic cladding is not a strong disturbance effect.

3. Conclusion By combining 3MA quantities with quantities derived from dynamic magnetostriction measurements using an EMAT the shift of DBTT on irradiated Charpy samples of base material and weldments of reactor pressure vessels of western and eastern design can be determined non-destructively. 3MA and EMAT-ultrasound signals can be measured through an austenitic cladding independent on microstructure changes in the cladding and the material beneath the cladding (base material/weldments). On the basis of these results the development of an inservice inspection technique is possible which allows determining the shift of the DBTT non-destructively directly on the inner diameter surface of the reactor pressure vessel.

Acknowledgement The funding of the Federal Ministry of Economics and Technology of Germany, reference number 1501352, is very much acknowledged. Thanks to AREVA NP GmbH and Research Center Dresden-Rossendorf e.V. for the supply of the Charpy specimens, the destructive tests and assistance at the investigations in the hot cell.

References [1] Altpeter, I., Becker, R., Dobmann, G., Kern, R., Theiner, W.A., Yashan, A.: Robust solutions of inverse problems in electromagnetic non-destructive evaluation, Inverse Problems 18, 2002, 1907-1921 [2] Wolter, B., Dobmann, G.: Micromagnetic testing for rolled steel, ECNDT 2006 Proceedings, Berlin, Sept. 25 - 29, 2006, Th.3.7.1 [3] Altpeter, I, Dobmann, G., Szielasko, K.: Nachweis von Cu-Ausscheidungen mittels mikromagnetischer Prüfverfahren. Abschlussbericht, BMWi Reaktorsicherheitsforschung, FKZ 1501219, GRS Forschungsbetreuung, Köln, IZFP-Bericht Nr. 020120-TW, 2002 [4] Hein, H., Keim, E., Schnabel, H., Seibert, T., Gundermann, A.: Final Results from the Crack Initiation and Arrest of Irradiated Steel Materials Project on Fracture Mechanical Assessments of Pre-Irradiated RPV Steels Used in German PWR, J. ASTM Int. 6, Paper ID JAI101962, 2009 [5] Altpeter I., Dobmann, G., Hübschen, G., Kröning, M., Verfahren zur Messung der Neutronenversprödung unterhalb der Plattierung von Druckbehältern, Patent Nr. WO 2008/135054

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In-Line Thin Film Characterization Using Eddy Current Techniques Susanne HILLMANN, Marcus KLEIN, and Henning HEUER Fraunhofer Institute for Nondestructive Testing Dresden, Germany Abstract. Thin films are successfully used in many different ways as functional layers in various areas of science, technology, and medicine. The coatings are produced using different methods, such as evaporating, sputtering, or chemical vapor deposition and have different properties, such as adhesion, specific electric resistance, and diffusion coefficient. For all applications, the analysis of coating thicknesses plays an important role, because most of the operating and performance characteristics are a function of the coating thickness. Here, in particular, are recognized in-line-methods, working contact-less, very fast, and in a vacuum. For coatings with thicknesses in the nanometer range and lower micrometer range, Eddy Current systems are especially well adapted. By using a special transmission mode sensor application, the method is very well suited for in-line inspections. Through optimization of the measuring system, sensors, and algorithms it is possible to largely widen the limits of the measurement system and to achieve very high accuracy. The following report presents results obtained with an Eddy Current measurement system working in transmission mode on samples with different single-layer and multi-layer coatings in the nanometer range. Keywords: Eddy Current transmission mode, thin film technology, film thickness

Introduction The studies reported here are motivated primarily by questions coming from the solar industry. In modern coating facilities various thin film layers with high and low conductivity and thickness ranges in the nanometer to micrometer scale are coated on substrates of glass, silicon, or foils. Process-related thicknesses cannot always remain constant, and therefore the coating thickness must be monitored in-line. For the in-line monitoring of the coating thickness the non-contact Eddy Current method is suitable because of its excellent potential for automation and high sensitivity to conductivity changes. This paper presents test results of the performance and efficiency of this method.

1. Measurement Method 1.1. Sensor Arrangement and Measurement Equipment The Eddy Current method can be applied with different sensor arrangements. For inline monitoring of thin, conductive layers, the transmission mode arrangement is very appropriate. In contrast to a surface probe, which locates the transmitting and receiving coil in one sensor body and is applied from one side of the samples surface, the coils in

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the transmission mode are separately arranged at a fixed distance from each other. The sample must be thin and flat and must be aligned between the sensors. Figure 1.a) illustrates a schematic of this application. It utilizes for both sensors identical singlecoils with a special core and 30 windings each. The coils have a width of 25 mm and excite a relatively large electromagnetic field. The advantage of this setup is the low influence of misalignment of the sample between the sensors on the test result, making this very practical for in-line inspections. Additionally, it is possible to achieve a larger distance between sensor and sample using the transmission mode [1,2]. In the solar industry, a large distance between sensor and sample is often required, especially when the solar cells in quite massive and prone to bending carriers are passed through the coating line. Therefore, the challenge is to develop a transmission arrangement with the greatest possible measuring gap of several centimeters in thickness at very high resolution (in the nanometer range).

a)

b)

Figure 1.a) Schematic illustration of the Eddy Current method at flat samples by use of transmission mode; 1.b) EddyCus TF® Eddy Current desktop system applying the transmission mode.

Using the EddyCus TF® system developed at Fraunhofer IZFP Dresden, the sensor-sensor distance can be increased up to 60mm, still maintaining a high thickness resolution. Figure 1.b) illustrates this device. All of the following presented measurements were performed with this device. 1.2. Optimum Measurement Frequency Especially for very small thicknesses, it is important to choose the optimal measurement frequency to establish a good separation between data from sample thickness variations and from conductivity variations. This is particularly important when process-related temperature changes may alter the conductivity of the sample. Depending on the measuring frequency, both material properties can be separated from each other in varying degrees; Figure 2 illustrates this coherence. The left diagram in figure 2.a) illustrates a common impedance plane diagram. Here, the measurement results on samples with different wall thickness and different conductivity can be very clearly separated in case of high wall thickness (lower area of the diagram). In case of very low wall thickness (higher area of the diagram) the curves run nearly congruent [3]. The diagrams in figure 2.b) illustrate the determination of angle Į as an instrument for describing the separation between conductivity and wall thickness. The schematic

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illustrates the points in the complex impedance plane for measurements at thin metal sheets of different thickness and conductivity. Point M1 is obtained by the measurement on a thin sheet with conductivity ı1 (e.g. aluminum) and the thickness d1. Measuring point M2 is generated by a measurement on a same material sheet (conductivity ı2=ı1), but higher layer thickness d2>d1. In contrast, the point M3 results from the measurement on a sheet of the primary thickness of d3=d1, but with a material of higher conductivity ı3>ı1 (e.g. copper). The left image shows this correlation at an unfavorable measurement frequency. Based on natural variations, the measurement points M2 and M3 are difficult to separate from each other. They are located very close to each other, because the impedance locus of conductivity and thickness are almost superimposed. The image on the right illustrates the complex impedance plane for the same samples at a suitable measurement frequency. In this case, points M2 and M3 are well separated from each other.

Figure 2.a) common impedance plane for different conductivity and wall thicknesses. 2.b) Schematic illustration of the complex impedance plane with an adverse measurement frequency f1, which produces poor separation of conductivity and thickness, and results in a small angle Į (left); a favorable measurement frequency f2 with a large opening angle Į is shown on the right.

A dimension for separability of both properties is the opening angle Į, located within the starting point M1 and points M2 and M3. The larger the angle Į, the better conductivity and coating thickness can be separated in the measurement signal, and small film thicknesses in the nanometer range can be obtained with high resolutions even at higher conductivity variations. Depending on the conductivity of the material, the opening angle Į generates its maximum at different measurement frequencies, whereas the frequency with the maximum angle increases with decreasing conductivity [3,4]. To determine the optimal measurement frequency for higher conductivity of around 50 MS/m, a series of experiments using thin metal sheets of aluminum (30 MS/m) and copper (56 MS/m) with different wall thicknesses of 10, 20 and 30 μm were performed. All samples were cut in a circle form from thin foils with a diameter of 100 mm. All samples were measured in transmission mode using several measurement frequencies ranging from 10 kHz to 1 MHz. The opening angle Į was calculated for each data set of different measurement frequencies. The results are illustrated in Figure 3. The maximum opening angle Į for the tested materials was established at a frequency at about 400 kHz, which can be used as the optimal

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measurement frequency for this conductivity range. This obtained optimum frequency is determined for the described measurement system in transmission mode for the used kinds of sensors. Each sensor- and measurement system and each conductivity range has its own optimum measuring frequency, whereas the optimum measuring frequency increases with decreasing film conductivity. [4] angle between thickness and conductivity 25

Cu

,d ͘

20

angle Į [°]

Alu, d ͘ Į

15 10 5 0 0,01

0,1

1

frequency [MHz]

Figure 3. Determination of optimal measurement frequency for high conductivity by calculating the opening angle Į from measured data using thin aluminum and copper sheets with different thicknesses

2. Single Layer Systems in the Nanometer Range 2.1. Description of the Samples For the validation of the measurement system, two sample sets with different conductive layers were prepared. Conductive layers with thicknesses between 5 nm and 205 nm were applied by sputtering on silicon wafers with a diameter of 100 mm and a thickness of 500 μm. For sample set 1 copper layers were used to evaluate the performance of high conducting layers. In contrast, sample set 2 was coated with Tantalum silicon nitride (TaSiN), which has a much lower conductivity then copper. The Table 1 lists all used samples, the intended film thickness d and the sheet resistance Rs obtained via the touching four-point method. Table 1. List of samples from sample set 1 and 2 including intended thickness d and sheet resistance Rs Sample set 1 (copper layer) Nr. d [nm] Rs [ȍ/͘] Cu-1 5 57,5 Cu-2 10 11,3 Cu-3 15 5,52 Cu-4 20 2,95 Cu-5 25 2,04 Cu-6 50 0,77 Cu-7 55 0,68 Cu-8 100 0,30 Cu-9 105 0,28

Nr. Ta-1 Ta-2 Ta-3 Ta-4 Ta-5 Ta-6

Sample set 2 (TaSiN-layer) d [nm] Rs [ȍ/͘] 10 455 15 307 50 98,6 55 93,8 200 27,9 205 26,8

Eddy Current measurements were performed on each sample with the EddyCus TF desktop system using an optimal measurement frequency. The measuring gap was varied between 20 mm and 60 mm, and the measurement was repeated eight times for

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each adjustment. In a first step, calibration curves were recorded to determine the Eddy Current parameter as a function of film thickness. Since there was an almost linear relationship between these two parameters, the calibration function was calculated using the measured values from samples with the lowest, middle and highest layer thicknesses. Using this calibration function, the film thicknesses of the remaining samples were obtained and the accuracy of the system was verified. 2.2. Results Obtained at Sample Set 1 – Copper Layer The calibration functions for sample set 1 (samples with copper layer) were obtained on samples Cu-1, Cu-5 and Cu-9. The film thickness measurement of the remaining samples using a measuring gap of 20 mm resulted in an average thickness accuracy of 1 nm. On samples with very thin copper layers of a maximum of 25nm, this high accuracy remains when the measuring gap is increased up to 60 mm. In contrast, the measurement accuracy decreases on samples with higher film thickness (starting at 50 nm) when increasing the measurement gap of up to 4 nm around the set point of the film thickness. Results from sample set 1 are shown in Figure 4. The diagram on the left shows the analyzed thickness values from all 8 repetitions obtained by the Eddy Current measurements as a function of the set point of the film thickness for a sensorto-sensor distance of 20 mm. The diagram on the right demonstrates the deviation from the set point of the film thickness for 3 sensor-to-sensor distances of 20 mm, 40 mm, and 60 mm. deviation from set point

copper layer on substrate of silicon

(copper layer)

sensor-sensor distance 20 mm deviation from set point [nm]

thickness (EC) [nm]

105 85 65 45 25 5

4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0

2 cm 4 cm 6 cm

10 5

25

45

65

85

105

15

20

50

55

100

thickness [nm]

thickness (set point) [nm]

Figure 4. Results of thickness measurements on sample set 1 (copper layer). Left diagram: Coating thickness as a function of the set point of the film thickness established by Eddy Current. Right diagram: Deviation of the film thickness set points for different sensor-to-sensor distances.

In a further experiment, the effects of position variations of the sample within the measuring gap on the established film thickness were investigated. Some of the copper samples were examined in a transmission mode system with a sensor-to-sensor distance of 40 mm. All samples were positioned in the center of the measuring gap, moved 5 mm up and tilted by 10°, whereas each measurement was repeated five times. The measurement positions are shown schematically in Figure 5.a); Figure 5.b) illustrates corresponding results and determined respective film thicknesses as a function of the film thickness set point. The measurement accuracy does not change when the sample is moved or tilted. There is a constant deviation from the desired set point of ± 3 nm for all three sample positions.

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copper layer on substrate of silicon at different sample positions

Send moved of 5 mm centre tilted by 10°

Receive

a)

thickness (EC) [nm]

110 90 70 50 30 10 10

30

b)

50

70

90

110

thickness (set point) [nm]

Figure 5.a) Schematic illustration of the sample positions tested in the measuring gap; 5.b) results of thickness measurement at different sample positions

2.3. Results Obtained at Sample Set 2 – TaSiN-Layer For sample set 2 (TaSiN layer), measurements similar to sample set 1 were taken. At these samples the optimal measurement frequency was higher, due to a significantly lower conductivity than the conductivity of the copper layered samples. The measurement accuracy was not as good as the accuracy obtained from the copper layered samples, which was expected due to lower conductivity. Figure 6 illustrates the calibration points obtained from sample set 2. It shows the phase of the complex Eddy Current signal as a function of the film thickness set points for a sensor-to-sensor distance of 20mm. The measurements for each sample were repeated five times.

Eddy Current phase [rad]

TaSiN-layer on substrate of silicon -1,1605 -1,1610 -1,1615 -1,1620 -1,1625 -1,1630 -1,1635 -1,1640 -1,1645 -1,1650 -1,1655 0

50

100

150

200

250

thickness (set point) [nm]

Figure 6. Calibration points for Eddy Current film thickness measurements of sample set 2, demonstration of the phase of the complex Eddy Current signal as a function of the film thickness set point.

It is clearly visible that measurement values with film thickness variation of 5 nm cannot be separated. However, the measurement values have a high reproducibility and the values around 10 nm, 50 nm, and 200 nm are very well separated. Using a calibration function, the coating thickness can be established in the same way as for sample set 1. Using a sensor-to-sensor distance of 20mm could achieve a measurement accuracy of 20 nm. With increasing sensor-to-sensor distance, the measurement accuracy decreases cumulatively. Here we can see the limit of the measurement system. Coatings with very low conductivity can only be measured adequately if a very small measuring gap is used or higher film thicknesses are investigated.

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3. Multi- Layer Systems in the Nanometer Range For the investigation of multi-layer coatings, we initially studied a system with two conductive layers. These samples consisted of a substrate of glass to which successive layers of zinc oxide (non-conductive), silver and aluminum were applied. The thicknesses of the conductive layers of silver and aluminum vary between 100 nm and 600 nm. Table 2 lists the samples and the appropriate coating thicknesses. Table 2. List of the samples of sample set 3 (multi layer) and their coating thicknesses Nr. multi-1 multi-2 multi-3 multi-4 multi-5 multi-6 multi-7

Thickness Silver [nm] 103 205 400 590 200 205 205

Thickness Aluminum [nm] 105 105 95 95 200 385 590

Total Thickness [nm] 208 310 495 685 400 590 795

When performing measurements in the transmission mode, the field always penetrates all layers as well as when using a surface probe; the entire layer will always be penetrated due to the very thin layers. This fact provided two measurement approaches: thickness measurements of the total thickness of both conducting layers, and second, thickness measurements of single layers. The results of both measurements are demonstrated in Figure 7. multi layer on substrate of glass

multi layer on substrate of glass

single layer

total thickness

500

thickness (EC) [nm]

thickness (EC) [nm]

800 700 600 500 400 300 200 200

300

400

500

600

700

thickness (set point) [nm]

800

450 400 350 300 250 200 silver aluminum

150 100 100

200

300

400

500

thickness (set point) [nm]

Figure 7. Coating thicknesses obtained by Eddy Current techniques as a function of the film thickness set point, measured on sample set 3 (multiple layers). Left: Measurements of total thickness (all layers). Right: Measurements of single layers

To determine the total thickness of the aluminum and silver layers, the calibration function was obtained using the measured values of the sample multi-1 (smallest total thickness) and multi-7 (maximum overall thickness). Using this almost linear function, the thickness values of the remaining samples were determined. A sensor-to-sensor distance of 40 mm was applied. A maximum deviation from the film thickness set point of 55 nm was achieved in this investigation. Since the amounts of aluminum and silver contents in the layers always vary, the total conductivity of the layer varies too, which explains the relatively high measurement error.

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In each case, measurements of single layer samples were performed with a constant sample set; one thickness of both layers. The analysis of the silver layer was attained with the multi-1 to multi-4 samples, whereas the calibration function was acquired with samples multi-1 and multi-4. Analysis of the aluminum layer was performed with samples multi-2 and multi-5 to multi-7, while the calibration function was attained with multi-2 and multi-7 samples. On the silver layer, a maximum deviation of the film thickness set point of ± 17 nm was be detected, and a maximum deviation of ± 38 nm was observed on the aluminum layer samples. The concept outlined in the section 3, shows again that the measurement accuracy is increasing with increasing layer conductivity. Under the assumption that only the thickness layer of one multi-layer film system varies while the other remains constant, the varying thickness of this layer can be accurately determined.

4. Summary and Outlook It was demonstrated that a large number of conductive layers of thin film technology can be characterized by Eddy Current testing. Table 3 summarizes the accuracy of all presented results. Table 3. Accuracy of the tested samples at different sensor-to-sensor distances, obtained in the Eddy Current transmission mode (EddyCus TF®) Single Layer Coating material copper TaSiN

Coating thickness range 5nm – 100nm 10nm – 200nm

Sensor-to-Sensor distance 20mm ± 1nm ± 20nm

Sensor-to-Sensor distance 40mm ± 1.5nm ± 50nm

Sensor-to-Sensor distance 60mm ± 2nm ± 100nm

Multi Layer Coating material silver aluminum total

Coating thickness range 100nm – 600nm 100nm – 600nm 100nm – 600nm

Sensor-to-Sensor distance 20mm ± 10nm ± 21nm ± 54nm

Sensor-to-Sensor distance 40mm ± 15nm ± 36nm ± 55nm

Sensor-to-Sensor distance 60mm ± 17nm ± 35nm ± 104nm

It was also revealed that the transmission mode is quite insensitive to sample position variations and thus presents a solid in-line testing method for thin film technology. The EddyCus TF® measurement system allows thickness measurement by using a sensor-to-sensor distance of up to 60 mm for highly accurate thickness measurement of conductive layers in the nanometer range. Measurement accuracy of 1 nm in the thickness range of 5 nm to 100 nm can be achieved on in highly conductive layers, such as copper. In addition, multi-layer systems can be accurately analyzed with this system. Under the assumption that only the thickness of the layers varies, the varying layer thickness can be determined very precisely. By selecting the best possible measurement frequency for each conductivity range, the accuracy of the measurement system can be optimized and changes in the conductivity of the samples caused by temperature variations, for example, can be easily separated from thickness variations. This makes the EddyCus TF® system a precise, fast, and automatable measurement

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system with a great potential for cost-effective thickness measurement of thin conductive layers.

References [1] [2] [3] [4]

K. Nitzsche, “Schichtmeßtechnik”, Vogel-Buchverlag, technical book, 1. Auflage, 1996, ISBN 3-80231530-8A.N. Author, Article title, Journal Title 66 (1993), 856–890. H. Heuer, S. Hillmann, M. Röllig, M. H. Schulze, K-J. Wolter, „Thin Film Characterization Using High Frequency Eddy Current Spectroscopy”, Conference on Nanotechnology, Genua, 2009 E. Hanke, “Prüfung metallischer Werkstoffe”, Band II, Zerstörungsfreie Prüfverfahren, VEB Deutscher Verlag für Grundstoffindustrie, Leipzig 1960, 2. überarbeitete Auflage A. Yashan, „Numerische Modellierung von Wirbelstromaufgaben und Lösung des inversen Problems“, ZfP-Zeitung 67, Oktober 1999

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-339

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Feasibility of stress state assessment on the grounds of measurements of the strength of the residual magnetic field of ferromagnetics a

Maciej ROSKOSZa,1 Silesian University of Technology, Poland

Abstract. The relations between stress and the values of the components of the residual magnetic field of ferromagnetic steels exposed to static and low cycle loads were examined. For static loads the measurements of the strength of the residual magnetic field were shown under load and after unloading. For low cycle loads, on the other hand, the impact of the number and the amplitude of changes in load were presented. It was concluded on the grounds of reference literature and the obtained results that the irreversible changes in magnetization, which result from loads, could be used as diagnostic signals. The tangential component which is parallel to the direction of tensile loads is characterized by a good correlation with stress. The fact that the value of the RMF increases significantly after yield stress is exceeded makes it possible to work out a method to determine areas with plastic strain. The conclusions presented seem to be a good starting point for further and deeper studies and analyses whose aim is to employ the strength of the residual magnetic field to assess the stress state of machine and construction components. Keywords. residual magnetic field, stress, magneto mechanical effect, control magnetic methods

Introduction There is a strict relationship between the magnetic and mechanical properties of ferromagnetic materials. The influence of stress on the magnetic properties is described by the magneto-mechanical effect. If a ferromagnetic is placed in a magnetic field, its level of magnetization varies according to loads. The change in magnetization has a reversible component, which fades after unloading, and an irreversible one. The level of magnetization depends on the type of material, the strength of the magnetic field, the magnetic history, strain and temperature [1 – 3]. The strength of the (RMF) is known to have been used as a diagnostic signal in flaw detection – the Metal Magnetic Memory Method [1 – 4]. The magnetic properties of steel and their use in diagnostics are the subject of many publications [4 – 14] The presented results are a part of studies whose main objective is to develop a system of a non-destructive assessment system of the technical condition and wear of 1 Institute of Power Engineering and Turbomachinery, Faculty Of Energy And Environmental Engineering, ul. Konarskiego 18, 44 100 Gliwice, Poland

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power machinery components subjected to typical loads such as low-cycle fatigue and creep. One of the tasks is an analysis of the possibility to use the changes in the magnetic properties of ferromagnetics as diagnostic signals for that purpose. The study focused on methods based on changes in the magnetization of components, and changes in the Barkhausen effect. It was assumed that the complementarity of the methods would allow a determination of stress distribution and wear that would be precise enough for industrial practice.

1. Objective and experimental details This publication presents the results of preliminary studies of changes in magnetization to determine: • The relations between stress and the values of the RMF components of ferromagnetics for static and quasi-static loads. • The impact of changes in the external magnetic field on the RMF of samples. • The impact of the stress amplitude and the number of cycles on the values of the RMF components of ferromagnetics. The research was conducted for ferromagnetic steel. The samples were not preliminarily demagnetized. The initial state of magnetization was a consequence of the history of their preparation and was not homogenous. The magnetometer TSC-1M-4 with the measuring sensor TSC-2M (Foerster type sensor) supplied by Energodiagnostika Co. Ltd Moscow was used for the measurements. As a result of the measurements, 3 values of the components of the RMF strength on the surface of the examined ferromagnetic samples were obtained: • Ht,x – tangential component measured in the direction perpendicular to the load applied, • Ht,y – tangential component measured in the direction parallel to the load applied, • Hn,z – normal component.

2. Static loads The geometrical form of the examined samples is shown in Fig. 1. The chemical constitution and the strength properties of the materials that the samples were made of are listed in Table 1.

Figure 1. Experimental sample.

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4 measuring sections of the same size were selected on a part of the sample. They were denoted as , , , . The division into measuring sections was introduced to check the repeatability of the relation: stress – the values of the RMF components. The points with symbols corresponding to the denotations of the measuring sections are average values of the RMF components for these sections. Table 1. Chemical constitution and strength properties of the sample material (R e yield stress, Rm stress)

ultimate

C

Si

Mn

Cr

Cu

Al

V

W

P

S

Re [MPa]

Rm [MPa]

max 0,22

0,10,35

max 1,1

0,3

-

-

0,3

-

0,05

max 0,05

280

380-520

Exemplary measurements of the RMF strength under load – grey lines, and after unloading – black lines, were shown in Fig. 2 to 4 as a function of the applied load. For each of the measuring sections the dependence of the average values (from 3 samples) on stress was approximated with a polynomial. 2.1. Measurements under load The trend of the changes in the values of the RMF components under loading is not constant, not even within elastic strain. The stress σ values at which it changes are characteristic of a given material. For components Ht,x and Hn,z the trends of the changes depend on the measuring section – the measuring point. This proves that there is no correlation between stress σ and the value of the component. However, in the analyzed cases the trend of the changes in component Ht,y did not depend on the measuring point, and was identical in all measuring sections. The greatest diversification of the values of components Ht,x and Hn,z in individual measuring sections occurs with stress σ approximating yield stress Re. 2.2. Measurements after unloading The representation of the impact of the load on the values of the RMF components measured after unloading is dominated by a decisive change in their values around yield stress Re. As for elastic strain, it can be assumed that there is a steady trend of changes in the values of the RMF components. After yield stress Re is exceeded, the trend of changes in both component Ht,x and component Hn,z is not identical and depends on the measuring point – the measuring section. 2.3. Impact of changes in the external magnetic field Fig. 5 shows the results of measurements of the RMF conducted after unloading on the surface of the sample inside a strength testing machine and outside it. A substantial quantitative change was observed, but the qualitative relations: stress – magnetization remain unchanged. It is due to the fact that the solution to the problem of allowing for the impact of the external magnetic field value is decisive when considering the sense of using RMF measurements for stress assessment.

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160 Ht,x [A/m]

  . 

120

80

40

0

-40 0

100

200

300

Figure 2. Relation between stress σ and component Ht,x, measurement under load after unloading black lines.

400

σ [MPa]

500

grey lines, measurement

500 Ht,y [A/m]

  . 

400

300

200

100

0 0

100

200

300

Figure 3. Relation between stress σ and component Ht,y, measurement under load after unloading black lines.

400

σ [MPa]

500

grey lines, measurement

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M. Roskosz / Feasibility of Stress State Assessment on the Grounds of Measurements 200 Hn,z [A/m]

0

-200

-400

  .  -600 0

100

200

300

400

Figure 4. Relation between stress σ and component Hn,z, measurement under load after unloading black lines.

σ [MPa]

500

grey lines, measurement

600 Ht,y [A/m]

  . 

400

200

0

-200 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

σ/Re

1.8

Figure 5. Impact of changes in the external magnetic field on the values of component Ht,y, measurement inside a strength testing machine black lines, measurement outside a strength testing machine grey lines.

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3. Cyclic loads Fatigue tests were conducted in the area of elastic strain. The measurement results presented in Fig. 6 to 8 refer to one kind of ferromagnetic steel which was subjected to loads where the value of the cycle asymmetry coefficient R was equal to 0, with different maximum stress of the cycle. Analyzing the obtained results it was found out that: • the greatest change in the values of the components occurred after the first load cycle • each subsequent load cycle produces smaller and smaller changes in the values of the components • the impact of the maximum stress of a cycle is visible. 20 Ht,x [A/m] 0

100 Ht,y [A/m] 0

-20 -40

σ1/Re= 0.4

-50

σ2/Re= 0.8

-100

-60

INITIAL STATE

-150 1

10

100

N

1000

Figure 6. Impact of changes in the number of cycles and maximum stress on the values of component Ht,x, of the RMF.

INITIAL STATE

1

10

100

N

1000

Figure 7. Impact of changes in the number of cycles and maximum stress on the values of component Ht,y of the RMF.

150

H

Hn,z [A/m] 50 0 -50 -100 -150

INITIAL STATE

1

10

100

N

1000

Figure 8. Impact of changes in the number of cycles and maximum stress on the values of component Hn,z of the RMF.

N Figure 9. Schematic correlation between the permanent change in magnetization and the number of load change cycles.

On the grounds of this study, together with [7, 10, 14], a schematic correlation between the changes in the RMF and the number of load change cycles was determined (cf. Fig. 9). In the beginning phase of the load process, and also just before the sample is destroyed, significant changes in the value of the RMF can be observed. In the

M. Roskosz / Feasibility of Stress State Assessment on the Grounds of Measurements

345

plateau phase, depending on the steel microstructure, there is a slight increase or decrease in magnetization.

4. Summary The paper presents preliminary results of a study of changes in the RMF strength caused by applied loads. On the grounds of the results it can be concluded that: • The tangential component which is parallel to the direction of tensile loads is characterized by a good correlation with stress. • The fact that the value of the RMF increases significantly after yield stress is exceeded makes it possible to work out a method to determine areas with plastic strain. • The irreversible changes in magnetization, which result from stress, can be used as diagnostic signals which make it possible to determine the stress state of ferromagnetics. Because of the special character of the stress – component Ht,y relation, the determination of the stress value is not possible with component Ht,y only. Analyzing the dependences between stress and the values of the RMF components it can be stated that it is possible to define the local stress state on the grounds of the values of component Ht,y and gradient Hn,z. [10] presents a good correlation between the distribution of component Ht,x with the distribution of shear stress, which can also be used to assess the state of stress. • There is a correlation between the level and number of load cycles, and the state of magnetization. A dramatic change in the value of the RMF occurs in the last phase of fatigue wear [7, 10, 14], which makes it possible to anticipate the destruction of the component. • The external magnetic field has a significant impact on the values of the RMF. The solution of the problem of how to account for this significance is decisive when considering the sense of using RMF measurements for stress assessment. The conclusions presented seem to be a good starting point for further and deeper studies and analyses whose aim is to employ the strength of the RMF to assess the stress state of machine and construction components.

Acknowledgements This work was supported by the Polish National Centre for Research and Development within the strategic program „Advanced Technologies for Energy Generation”

References [1] [2]

Deputat J.: Basics of the Metal Magnetic Memory Method. Dozór Techniczny 5/2002 p. 97 105. (in Polish) Jiles D. C., Theory of the Magneto Mechanical Effect, J. Phys. D: Appl. Phys., 28 (1995) 1537 1546.

346

[3]

[4]

[5] [6] [7]

[8]

[9] [10] [11]

[12]

[13]

[14]

M. Roskosz / Feasibility of Stress State Assessment on the Grounds of Measurements

Dubow A.A.: Principal Features of Metal Magnetic Memory Method and Inspection Tools as Compared to Known Magnetic NDT Methods. WCNDT 2004, Montreal Canada, http://www.ndt.net/article/wcndt2004/papers/359.ntm John Wilson, Gui Yun Tian, Simon Barrans: Residual Magnetic Field Sensing for Stress Measurement and Defect Detection, Sensors and Actuators A: Physical, Volume 135, Issue 2, 15 April 2007, Pages 381 387 €urek Z. H. Magnetic Contactless Detection of Stress Distribution and Assembly Defects in Constructional Steel Element NDT&E International 38 (2005) 589 595 Augustyniak B., Degauque J. Magneto Mechanical Properties Evolution of Fe C Alloy during Precipitation Process, Materials Science and Engineering A 370 (2004) 376 380 Dobmann G., Lang M. On line Monitoring of Fatigue in the LCF and HCF Range by Using Micro magnetic NDT at Plain Carbon and Austenitic Stainless Steel, 8th ECNDT Proceedings TOC European Conference on Nondestructive Testing Barcelona (Spain), June 17 21, 2002 R. Sabet Sharghi, L. Clapham, D.L. Atherton, T.M. Holden The Effect of Defect Introduction vs. Load Application Sequencing on Defect Induced Stress Distributions in Steel Samples NDT&E International 33 (2000) 201 212 M. Soultan, X. Kleber_, J. Chicois, A. Vincent Mechanical Barkhausen Noise during Fatigue of Iron NDT&E International 39 (2006) 493 498 Roskosz M. Gawrilenko P, Analysis of Changes in Residual Magnetic Field in Loaded Notched Samples, NDT&E International 41 (2008) 570 576 Roskosz M: Possibilities of the Application of the Metal Magnetic Memory Method to the Analysis of Gear Durability. 9th European Conference on Non Destructive Testing ECNDT Berlin 2006, Abstracts Part 2, P 85 Roskosz M.: C‚ƒ†‡ƒˆ‡ ‰‡Š‹Œ ƒ‘’“Š‡ƒˆ‡‰ ˆ ƒ‘’“Š‡ƒƒ”‚•– ”—”‚˜‡ƒƒ™ ‰™ƒˆ‚ƒ™ ‘š“ ›‡’’‰™ƒ‡‚ˆœ˜, “‚“ ‰‡Š‹Œƒ’‹ƒ“ ƒŒžƒ ‚‡Ÿƒˆž‡”œ“ œƒ›‡’‡ƒ ˆ“ "¡ˆ™ƒ”‚ˆœ —’Œ‹˜ƒˆ“ ˆ œƒ”‚’Œœ ˆ¢ ” ˆ”‘š•£˜ƒˆ‡‰ ‰™ƒˆ‚ƒ¢ ‘‰“‚ˆ ‰‡‚šš", ¤”œ˜ 2009 pp. 53 61 Dong Lihong, Xu Binshi, Dong Shiyun, Chen Qunzhi, Wang Dan Variation of Stress Induced Magnetic Signals during Tensile Testing of Ferromagnetic Steels NDT&E International 41 (2008) 184 189 Yang En, Li luming, Chen Xing: Magnetic Field Aberration Induced by Cycle Stress, Journal of Magnetism and Magnetic Materials 312 (2007) 72 77

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Magnetic Characterization of Material Degradation Using Dynamical Minor Loops Satoru KOBAYASHI a,1 , Shinichi TSUKIDATE a , Hiroyuki OKAZAKI a , Yasuhiro KAMADA a Hiroaki KIKUCHI a , and Toshihiro OHTANI b a NDE and Science Research Center, Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan b Department of Mechanical Systems Engineering, Shonan Institute of Technology, Fujisawa 251-8511, Japan Abstract. We have examined scaling laws in dynamical magnetic minor hysteresis loops of Cr-Mo-V steel subjected to creep and cold-rolled low carbon steel in order to investigate the applicability to online evaluation of materials degradation in ferromagnetic steels. Although scaling laws in the medium magnetization range found previously fail in the high magnetization frequency regime owing to a significant contribution of eddy currents, a scaling power law of the relation between remanence and remanence work of minor loops holds true in a very low magnetization regime, irrespective of magnetization frequency as well as investigated materials. The coefficient of the law exhibits a good correlation with creep damage and rolling reduction and is proportionally related to Vickers hardness. These observations clearly demonstrate that the analysis of dynamical minor loops enables us to evaluate materials degradation in a short measurement time with low measurement field and high sensitivity to defect density. Keywords. Dynamical hysteresis loop, Creep damage, plastic deformation, Cr-MoV steel, low carbon steel, Nondestructive evaluation

Introduction Non-destructive evaluation (NDE) of aging degradation of structural materials has been carried out for a long time. Various techniques using eddy current, ultrasonic wave, Xray, magnetic powder etc., are now mature and widely used. Generally, these techniques are effective for detecting cracks with dimension greater than 0.1 mm. Nevertheless, none of NDE techniques have been employed so far as a standard method to evaluate degradation before initiation of cracking. Magnetic method using minor hysteresis loops has several advantages to get information on lattice defects in ferromagnetic steels. Our previous studies in plastically deformed low carbon steels [1] revealed that there exist several scaling power laws between 1 Corresponding Author: Satoru Kobayashi, NDE and Science Research Center, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan, E-mail: [email protected] .

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S. Kobayashi et al. / Magnetic Characterization of Material Degradation

Table 1. Chemical compositions of Cr-Mo-V steel (ASTM A193-B16). (wt. %) C

Si

Mn

P

S

Cr

Mo

V

Fe

0.420

0.290

0.66

0.016

0.009

1.090

0.51

0.28

Bal

Table 2. Chemical compositions of cold-rolled low carbon steel. (wt. %) C

Si

Mn

Fe

0.16

0.20

0.44

Bal

parameters of quasi-static minor loops in a medium range of magnetization over which irreversible movement of Bloch wall dominates magnetization process. The power-law relations include

∗ nF Ma ∗ 0 WF = WF , (1) Ms WR∗

=

WR0

MR∗ MR

nR ,

(2)

where WF∗ , WR∗ , Ma∗ , and MR∗ are hysteresis loss, remanence work, maximum magnetization, and remanence of minor loops, respectively, and the definition is given in the inset of Fig. 2(c). M s and MR are saturation magnetization and remanence of the major loop, respectively. The exponents n F and nR are approximately 1.5 and universally independent of temperature, stress, and kinds of ferromagnetic materials [1,2]. The coefficients WF0 and WR0 are a sensitive indicator of internal stress and can be obtained with low magnetic fields, typically less than 2 kA/m, which is far less than saturation field of > 10 kA/m. When one applies this method to online NDE of ferromagnetic components, however, it is necessary to reduce the measurement time; the measurement time to obtain coefficients for one condition is considerably long (15-30 min) due to low magnetization frequency below 0.1 Hz. Measurement with a higher magnetization frequency is one of the solutions to reduce the measurement time. It would be therefore useful to examine the scaling rules in the high frequency regime to investigate the applicability for magnetic NDE. In this study, we have investigated scaling rules of dynamical minor hysteresis loops for Cr-Mo-V steels subjected to creep as well as cold-rolled low carbon steels, varying the level of creep damage and plastic deformation, respectively.

1. Experimental Procedure The chemical compositions of crept Cr-Mo-V ferritic steel and low carbon steel are listed in Table 1 and 2, respectively. The Cr-Mo-V steel, which is widely used for high-temperature power plant components such as steam pipes, pressure vessels, was taken from a commercial plate of ASTM A193-B16. The creep tests were performed at 923 K in air under applied tensile stress of 35 MPa. Twelve specimens with different life fractions t/t r were prepared; t and t r are creep time and rupture life, respectively. Figure 1 shows creep strain and Vickers

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349

hardness as a function of t/t r . The creep strain increases with t/t r , whereas the Vickers hardness decreases. Both properties exhibit three creep deformation regimes; primary (0≤ t/tr <0.2), steady (0.2< t/t r ≤0.5), and ternary (0.5< t/t r ) stages. The details of the creep tests are given in previous works [3,4,5]

Figure 1. Creep strain and Vickers hardness as a function of life fraction t/tr for Cr-Mo-V steel.

The low carbon steel was cold rolled at room temperature. Five samples with different rolling reductions i.e. 0, 5, 10, 20, 40%, were prepared. Microstructural observations with transmission electron microscopy showed that dislocation density is low and dislocations are distributed homogeneously before the cold rolling, whereas dislocation cells are formed and the dislocation density becomes to be more than 10 10 cm−2 after 20% rolling reduction [1]. For magnetic measurements, the Cr-Mo-V and cold-rolled samples were cut into toroidal shapes and frames, respectively, and an exciting and a pickup coil were wound around the samples. A triangular current was applied to the exciting coil to generate a cyclic magnetic field and magnetize the sample. The magnetic field within the sample was obtained from the voltage across a 1-Ω resistance connected to the exciting coil in series. The induced voltage of the pickup coil was integrated in order to obtain a magnetic flux within the sample. A set of magnetic minor hysteresis loops with various field amplitudes Ha up to 8 kA/m was measured by gradually increasing the amplitude of the wave current. The frequency of a cyclic field was 0.05−300 Hz. Before measuring each minor loop, the sample was demagnetized with a decaying alternating magnetic field with a frequency of 10 Hz. 2. Experimental Results 2.1. Cr-Mo-V steel Figure 2 shows a set of minor hysteresis loops before and after creep tests, taken at various frequencies of a cyclic field. The loop width of minor loops with the same field

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Figure 2. A set of minor hysteresis loops measured before and after creep tests for Cr-Mo-V steel, taken at various magnetization frequencies; (a) 0.05 Hz, (b) 10 Hz, and (c) 100 Hz at t/tr = 0 and (d) 0.05 Hz, (e) 10 Hz, and (f) 100 Hz at t/tr = 0.80. Only representative loops are given for clarity. The inset in (c) denotes parameters of a minor hysteresis loop, measured with a field amplitude of Ha .

amplitude Ha becomes smaller after the creep tests for all the frequencies. The decrease of the loop width as the creep progresses may reflect the increase in the cell or subgrain size during creep [5]. With increasing magnetization frequency, the loop width becomes wider considerably owing to the increasing in the dynamical hysteresis loss due to eddy current [6]. For each minor loop, the parameters such as hysteresis loss W F∗ and maximum magnetization M a∗ were obtained and the dependence of the relations on frequency was examined in detail. Figures 3(a) and 3(b) show the double logarithmic plots of the relation between W F∗ and Ma∗ , before and after the creep tests. For a quasi-static condition of 0.05 Hz, the relation shows a straight line in a limited M a∗ range; μ0 Ma∗ = 0.2−1.2 T. Least-squares fits of data at 0.05 Hz to Eq. (1) yielded a power-law exponent of n F = 1.58 ± 0.02 for all the samples, being consistent with our previous works [5]. With increasing frequency, however, the slope in the double logarithmic plots increases and n F attains 1.78 ± 0.06 at the maximum frequency of 300 Hz as shown in Fig. 4(a). Such a strong dependence on frequency was also seen in the relation between W R∗ and MR∗ in a limited MR∗ range of 0.1−1.1 T (M a∗ = ∼ 0.2−1.2 T) as shown in Figs. 3(c) and 3(d); from least-squares fits to Eq. (2), n R was found to increase from 1.47 to 1.63 with increasing frequency from 0.05 to 300 Hz as shown in Fig. 4(b). The value of exponents n F and nR strongly depends on magnetization frequency and is not constant. This means that the scaling power laws obtained in a quasi-static condition (<0.1 Hz) are not universal in the higher frequency regime. This is due to the fact that the increase of the magnetization frequency results in the increase in the intensity of eddy currents induced during Bloch wall movement and therefore the increase in the dynamical hysteresis loss [6]. The eddy current effects are much pronounced in the

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351

Figure 3. Double logarithmic plots of relation between WF∗ and Ma∗ for (a) t/tr = 0 and (b) t/tr = 0.80, and ∗ and M ∗ for (c) t/t = 0 and (d) t/t = 0.80 for crept Cr-Mo-V steels, taken at various relation between WR r r R magnetization frequencies.

Figure 4. Frequency dependence of power-law exponents (a) nF and (b) nR for crept Cr-Mo-V steels, obtained from least squares fits to data in a medium Ma∗ range; μ0 Ma∗ = 0.2−1.2 T, where irreversible motion of Bloch walls dominates magnetization process. (c) Frequency dependence of power-law exponent nRL for ∗ range; μ M ∗ = 0.001−0.02 T, crept Cr-Mo-V steels, obtained from least squares fits to data in a low MR 0 R which typically corresponds to μ0 Ma∗ = 0.01−0.1 T.

medium Ma∗ range where irreversible movement of Bloch walls dominates the magneti-

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zation process and the magnetization shows a steep increase with field. On the other hand, in a low μ 0 MR∗ region below approximately 0.02 T, the slope of the relation between W R∗ and MR∗ , plotted on a double logarithmic scale, is weakly frequency dependent for all the crept samples as shown in Figs. 3(c) and 3(d), whereas that between WF∗ and Ma∗ in a low magnetization regime changes considerably with frequency as shown in Figs. 3(a) and 3(b). Least-squares fits of the W R∗ − MR∗ curves for μ0 MR∗ < 0.02 T to Eq. (2) yielded the exponent of n RL = 1.89 ± 0.03, which is independent of magnetization frequency and life fraction as shown in Fig. 4(c). Here, the subscript "L" is added to distinguish the low field data from the data in a medium magnetization range.

0 as a function of t/t for crept Cr-Mo-V steels, taken at various Figure 5. (a) Minor-loop coefficient WRL r 0 and Vickers hardness for crept Cr-Mo-V steels, taken magnetization frequencies. (b) Relation between WRL at various magnetization frequencies.

0 Figure 5(a) shows a minor-loop coefficient W RL as a function of t/t r for several magnetization frequencies, obtained from the least-squares fits. Here, the stage I, II, and III correspond to the primary creep, secondary creep, and tertiary creep, respectively, which were determined from the variation of the creep strain rate [3,4]. As the creep 0 sharply decreases at the stage I and shows a slight increase in the stage progresses, WRL II, followed by a steady decrease at the stage III for all the frequencies. This trend is consistent with our previous results for the medium magnetization range, obtained in a quasi-static condition of 0.05 Hz [5]. This behavior is very similar to that of Vickers 0 is roughly proportional to Vickers hardness for all hardness shown in Fig. 1 and W RL the frequencies as shown in Fig. 5(b), which is a sensitive indicator of creep damage. These observations strongly indicate that the creep damage can be evaluated in a short measurement time using the scaling power law of dynamical minor hysteresis loops; measurement time is approximately a few hundreds of milliseconds if a magnetization frequency is 100 Hz and a few dozens of minor loops with different H a are used for analysis. 0 and hardness with t/t r was interpreted by an increase Note that the decrease of W RL in the cell or subgrain size as well as the migration of dissolved carbon. The detailed discussion is given in previous studies [3,4,5].

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353

2.2. Cold-rolled low carbon steel A set of minor hysteresis loops were measured at magnetization frequencies from 0.05 to 300 Hz, and the scaling relations between the parameters were examined. As in the case of the Cr-Mo-V samples, both the W F∗ − Ma∗ and WR∗ − MR∗ curves in a medium Ma∗ range (μ0 Ma∗ = 0.2−1.2 T) depend on magnetization frequency and the obtained exponents n F and nR steady increase with increasing the frequency; as the frequency increases from 0.05 to 300 Hz, n F changes from 1.59 to 1.85, whereas n R changes from 1.53 to 1.79. On the other hand, the W R∗ − MR∗ curve in a low M a∗ range is weakly dependent of frequency and the least squares fits gave n RL = 1.80 ± 0.04 for all the cold rolled steels. This value is close to that of crept Cr-Mo-V samples.

0 as a function of rolling reduction for cold-rolled steels, taken at various magnetization Figure 6. (a) WRL 0 and Vickers hardness for cold-rolled steels, taken at various magnetifrequencies. (b) Relation between WRL zation frequencies.

0 Figure 6(a) shows the minor-loop coefficient W RL as a function of rolling reduction, 0 taken at various frequencies. For all the frequencies, W RL monotonically increases with reduction at almost the same rate and exhibits a linear relationship with Vickers hardness 0 as shown in Fig. 6(b). The increase of W RL and Vickers hardness with reduction is attributed to an increase of dislocation density with rolling reduction [1]. These results clearly show the validity of the scaling power law of dynamical minor loops in the low magnetization regime also for cold rolled steels.

3. Summary Scaling laws of magnetic minor hysteresis loops have been examined for crept Cr-Mo-V steel and cold-rolled low carbon steel, varying magnetization frequency from 0.05 Hz (quasi-static) to 300 Hz. As in the case of quasi-static condition, there exist scaling power laws between the parameters of dynamical minor loops in the medium magnetization range, where irreversible motion of Bloch walls dominates the magnetization process. However, the exponents strongly depend on the magnetization frequency and increase considerably with the frequency because of the increasing dynamical hysteresis loss due to eddy currents. On the other hand, in the low magnetization regime, the relation be-

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tween the remanence and the remanence work exhibits a power law with an exponent of 1.8−1.9, which is independent of magnetization frequency, defect density, and investigated materials. The coefficient of the law changes depending on defect density and exhibits a good correlation with mechanical property. By using scaling laws in the high frequency regime, measurement time to obtain the coefficient for one condition is drastically reduced to a few hundreds of milliseconds from a few tens of minutes in a quasistatic condition. The present studies open up a new possibility of online NDE of material degradation in ferromagnetic steels using dynamical minor hysteresis loops.

References [1] [2] [3] [4] [5] [6]

S. Takahashi, S. Kobayashi, H. Kikuchi, and Y. Kamada, J. Appl. Phys. 100 (2006) 113908. S. Kobayashi, T. Fujiwara, S. Takahashi, H. Kikuchi, Y. Kamada, K. Ara, and T. Shishido, Philos. Mag. 89 (2009) 651. T. Ohtani, F. Yin, and Y. Kamada, Jpn. J. Appl. Phys. 47 (2008) 3916. T. Ohtani, H. Ogi, and M Hirao, Acta Mater. 54 (2006) 2705. S. Kobayashi, M. Tanaka, T. Kimura, Y. Kamada, H. Kikuchi, S. Takahashi, and T. Ohtani, Studies in Applied Electromagnetics and Mechanics, 32 (2009) 240. G. Bertotti, in Hysteresis in Magnetism, (Academic press, San Diego 1998).

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-355

355

Local Magnetic Properties and Magnetic Particle Distribution due to Cr Depletion in Sensitized Ni based Alloy K. Yamaguchi a,1, K. Suzuki a, T. Takase a, T. Takara a, O. Nittono a, T. Uchimotob and T. Takagi b a Faculty of Symbiotic Systems Science, Fukushima University, Fukushima, Fukushima 960-1296, Japan b Institute of Fluid Science, Tohoku University, Sendai, Miyagi 980-8577, Japan

Abstract. For Alloy 600 which is Ni based super alloy, the relation between sensitization and magnetic properties was studied from the view point of chromium depletion distribution. Experimental results of magnetic hysteresis (B H) curves were compared with calculation results by Monte Carlo simulation including the information of the chromium depletion and both results showed good correspondence each other for their residual magnetizations and magnetic coercivities. Moreover, local magnetic hysteresis was measured by micro Kerr magnetometer for the area of inner grain and on grain boundaries. The result showed anisotropy on grain boundaries for the direction of magnetic field. The result is analyzed using a magnetic cluster formed as wire type which was derived from the chromium distribution estimated by energy dispersive X ray spectroscopy of scanning electron microscope. Keywords. Monte Carlo methods, nondestructive evaluation, Inconel, Cr depletion, magnetic hysteresis curve

Introduction Ni based super alloys, such as Alloy 600 (Inconel), are widely used as structural materials because of their high mechanical strength, e.g. in nuclear power plants, and therefore early detection of the fatigue of the materials is very important. It is known that the sensitization of Alloy 600 due to chromium depletion near grain boundaries by heat treatment causes the intergranular stress corrosion cracking (IGSCC), then especially the behavior under the sensitization has been studied as pressing matters [1][3]. It has been also known that the sensitization produces the magnetism in Alloy 600 which has no magnetism originally [4]-[5]. Recently the relationship between magnetic properties and sensitization is being studied to potentially use it as a basis for nondestructive evaluation (NDE) of the material [6]-[7]. Several experimental reports show the magnetization occurs at Cr depletion areas around grain boundaries and the degree of sensitization affects the magnetic properties such as magnetic hysteresis (BH) curves. However, how the distribution of Cr depletion affects the change of magnetism in Alloy 600 microscopically is not well understood, although the 㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷㩷 1

Corresponding Author. K. Yamaguchi (e mail: [email protected] u.ac.jp).

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relationship between the distribution of Cr depletion and the local magnetism around grain boundaries needs to be understood in order to estimate of the degree of sensitization using magnetic NDE. In this paper, local magnetic properties of sensitized Alloy 600 were measured using the micro Kerr effect and the experimental results are discussed comparing the results with simulated results obtained using the Monte Carlo (MC) method. By comparing the calculation results with experimental data, we lay down the basis of a MC method for detecting the degree of sensitization including the distribution of Cr depletion.

Analysis Method A cubic system composed of 313 cells (0,x,30, 0,y,30, 0,z,30) was prepared including magnetic sites with a certain distribution. The distribution was decided by Cr depletion degree around a grain boundary on the supposition that Cr depletion introduces magnetic moments around the depletion area [4]-[5]. The distribution of Cr depletion, which depends on the heating duration time, was calculated using thermodynamic analysis [8]-[12]. Here the heating duration time means the period of thermal annealing under a constant heating temperature. Figure 1(a) shows the calculation results of the distributions of magnetic site due to Cr depletion with each duration time (1h, 25h, 150h) under the heating temperature at 650 Celsius degree. The distributions of magnetic sites along x-axis of the cubic system for duration time of 25h is shown in Fig.1(b) as the surface view of the clusters. Here, the black circles represent the magnetic sites produced with a probability obeying the distribution of Cr depletion and white circles are non magnetic sites. In Fig.1(b), the grain boundary is set on the yz plane at the x-coordination of 15 and the edge surface coordination x=0 and x=30 are regarded as -300nm and +300nm respectively. A following Hamiltonian was used for the simulation:

H

HJ  HD  HB  S S  i j J S S  D $ $ ij ij j 3  all  r near ij 

3 rij

5

S

 (1)  

  r S  r i ij j ij   B $ S i .  i 

HJ term, HD term and HB term represent exchange interaction energy, magnetic dipole interaction energy and applied magnetic field energy, respectively. Here Si denotes the magnetic moment of the magnetic site of i-th cell and rij represents the vector between i-th site and j-th site. Below we deal with clusters with the lattice constant of 1 and this is regarded as a criterion of length. In the first term HJ, Jij stands for an exchange interaction energy constant for i-th and j-th sites. In the second term HD, D stands for a magnetic dipole interaction constant. The magnetic dipole interaction works on all magnetic sites because it is due to magnetic field interspersed in all space. The summation includes the interaction energy between i-th site and all j-th sites except for the case j=i. In the third term HB, B represents applied magnetic field which acts equally all magnetic sites. The changing of Si on MC simulation progresses as spinflips by Metropolis sampling at finite temperature kBT [13]-[14]. The period that N

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357

times of the spin-flips occur is called 1 MC step (MCS) for the number of magnetic sites N and it corresponds to time passage in this simulation. For details of MC method for magnetic dynamic process, see the references [15]-[23]. In this simulation, the parameters were set as Jij =1.0, D=0.01. The value of Si was fixed as |Si|=1.

Figure 1. (a) Distribution of magnetic sites due to Cr depletion as a function of distance from a grain boundary for each heating duration time. (b) Example of a cluster including magnetic sites for a duration time of 25h.

Results and Discussion Figure 2(a) shows the experimental results of the magnetic B-H curves for Alloy 600 with different duration times under the heating temperature at 650 Celsius degree. The measurements were performed at room temperature using a vibration sample magnetometer (VSM). On the other hand, Fig. 2(b) shows the calculation results of BH curves. The results of calculated B-H curves are the average of magnetization for two directions of applied magnetic field along perpendicular (x direction) and parallel (y direction) to grain boundary surface of cubic system. The behaviors of calculated BH curves for duration times correspond to the experimental ones, especially for the residual magnetization Mr and magnetic coercivity HC. Figure 3(a) and 3(b) show the heating duration time dependence of Mr and HC, respectively, including more different duration times. The calculation result shows good correspondence with the experimental data. The little difference of the duration time at Mr maximum between calculation and experiment can be due to the poor reliability of the estimated distribution of magnetic site due to Cr depletion in Fig.1(a). The calculation results of the duration time dependence of Mr and HC tell us the relation between the distribution of Cr depletion and the magnetic properties. As shown in Fig.1(a), the total amount of Cr depletion, i.e. the integral of the distribution, is the most for the duration time of 25h, and ones for 1h and 150h are almost same each other. Comparing B-H curves in Fig.2, Mr reflects the total amount of Cr depletion. On the other hand, the concentration of Cr depletion around a grain boundary is the most for the duration time of 25h, and the least for 150h as shown in Fig.1(a). Therefore HC depends on the average density of Cr depletion around grain boundaries.

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Next local magnetic B-H curves were measured by micro Kerr magnetometer (Neoark BH-L920V). Figure 4(a) shows a B-H curve at a point in a grain in sensitized Alloy 600 with duration time of 100h under the heating temperature at 650 Celsius degree and the result shows no magnetizations. Figure 4 (b) and (c) are B-H curves for same sample at the points on grain boundaries parallel and perpendicular to the applied magnetic field direction respectively. Micro Kerr magnetometer shows B-H curve without quantitative criterion of magnetization (e.g. unit of emu or T), but can tell the difference of magnetic properties relatively. The results indicate a magnetic anisotropy depending on grain boundary directions. To study the magnetic anisotropy properties more deeply, the distributions of Cr depletion around grain boundaries were measured using a scanning electron microscope (SEM). Figure 5(a) shows scanning electron micrograph of sensitized Alloy 600. In this figure, two circles show carbon condensations on a grain boundary. Figure 5(b) and (c) show distribution of Cr component measured by Energy Dispersive X-ray Spectroscopy (EDX) along each line A, B and C in Fig. 5(a). In Fig. 5(b), the distribution of Cr component along line A has a dip around the center of the boundary, on the other hand, along line B it shows a peak on the carbon condensation. These results mean the transference of Cr from boundary to carbon as well known in previous works by several authors. In Fig. 5(c), the distributions of Cr component along line C were measured using two different applied voltages of the electron beam for EDX. Line C is set on grain boundary between two carbon condensations. The distribution along line C shows Cr depletion occurs to the extent of about 200nm from carbon condensations along the boundary and Cr component rate is recovered in the area over the distance of 200nm. Moreover Fig. 5(c) shows Cr depletion rate measured using applied voltage of 10kV is larger than 15kV. In general, EDX measurement with higher voltage detects the elements in deeper region from the surface. Then the results show Cr depletion just occurs near the surface around a grain boundary. Then a magnetic cluster was formed as shown in Fig. 6. The cluster is reflected in the results of the distribution of Cr depletion, that is, it has a narrow width and a thin depth compared with the length along a grain boundary. Figure 4(d) shows the calculation results of BH curves applied the magnetic field parallel (z direction) and perpendicular (x direction) in Fig. 6 and the results show shape magnetic anisotropy. As a result, the anisotropy as shown in Fig.4 (b) and (c) will be caused as the shape effect due to the distribution of Cr depletion. As shown in above discussion, B-H curves for sensitized Alloy 600 include the information of the distribution of Cr depletion and it can even tell the local dispersion of Cr depletion around carbon condensations.

Figure 2. B H curves of (a) experiment and (b) calculation for each duration time.

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㩷 Figure 3. Duration time dependence of residual magnetization Mr and coercivity HC for (a) experiment and (b) calculation results.

Figure 4. (a) (c) Experimental results of B H curves for sensitized Alloy 600 under thermal aging with 100 hours heating duration time and (d) calculation results of B H curves by MC method for a cluster as shown in Fig.6. Experimental B H curves were measured using Kerr effect at each point: (a) in a grain, on a grain boundary (b) parallel and (c) perpendicular to the magnetic field direction. (d) Calculated B H curves are applied the magnetic field parallel (z direction) and perpendicular (x direction) in Fig. 6.

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Figure 5. (a)Scanning electron micrograph of sensitized Alloy 600. Circles show carbon condensations on a grain boundary. (b) (c) Distribution of Cr component along each line A, B and C in Fig.5(a).

Figure 6. Surface view of model cluster including magnetic sites due to the distribution of Cr depletion.

Conclusion The magnetization properties of sensitized Alloy 600 were analyzed using the Monte Carlo (MC) method including the distribution of Cr depletion. The experimental and

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computational results show good correspondence with each other, especially for Mr and HC. This shows that the magnetic properties are indicative the distribution of Cr depletion which can be obtained through MC simulation. The analysis allows one to use magnetic NDE to estimate the degree of sensitization.

References [1] M. Kowaka, H. Nagano, T. Kudo and Y. Okada, Effect of Heat Treatment on The Susceptibility To Stress Corrosion Cracking of Alloy 600, Nuclear Technology 55 (1981), 394 404 [2] J. D. Wang and D. Gan, Effects of grain boundary carbides on the mechanical properties of Inconel 600, Materials Chemistry and Physics 70 (2001), 124 128 [3] W.E.Mayo, Predicting IGSCC/IGA susceptibility of Ni Cr Fe alloys by modeling of grain boundary chromium depletion, Materials Science and Engineering: A 232 (1997), 129 139 [4] R. G. Aspden, G. Economy, F. W. Pement and I. L. Wilson, Relationship Between Magnetic Properties, Sensitization, and Corrosion of Incoloy Alloy 800 and Inconel Alloy 600, Metallurgical Transactions 3 (1972), 2691 2697 [5] S. Takahashi, Y. Sato, Y. Kamada and T. Abe, Study of chromium depletion by magnetic method in Ni based alloys, Journal of Magnetism and Magnetic Materials 269 (2004), 139 149 [6] S. Takahashi, H. Sato, Y. Kamada, K. Ara and H. Kikuchi, A new magnetic NDE method in inconel 600 alloy, IOS Press 19 (2004), 3 8 [7] R. Oikawa, T. Uchimoto, T. Takagi, Evaluation of sensitization of Ni base alloys using electromagnetic nondestructive evaluation method, Transactions of the Japan Society of Mechanical Engineers. A 75 (2009), 1777 1783 [8] D. D. Pruthi, M. S. Anand and R. P. Agarwala, Diffusion of Chromium in Inconel 600, Journal of Nuclear Material 64 (1977), 206 210 [9] G. S. Was and R. M. Kruger, A thermodynamic and kinetic basis for understanding chromium depletion in Ni Cr Fe alloys, Acta Metallurgica 33 (1985), 841 854 [10] M. Grujicic and S. Tangrila, Thermodynamic and kinetic analyses of time temperature sensitization diagrams in austenitic stainless steels, Materials Science and Engineering A142 (1991), 255 259 [11] J. J. Kai, C. H. Tsai and G. P. Yu, The IGSCC, sensitization, and microstructure study of Alloys 600 and 690*, Nuclear Engineering and Design 144 (1993), 449 457 [12] G. Bao, K. Shinozaki, M. Inkyo, T. Miyoshi, M. Yamamoto, Y. Mahara and H. Watanabe, Modeling of precipitation and Cr depletion profiles of Inconel 600 during heat treatments and LSM procedure, Journal of Alloys and Compounds 419 (2006), 118 125 [13] N. Metropolis, A. Rosenbluth, M. Rosenbluth, and A. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21 (1953), 1087 1092 [14] D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press. (2000),68 73 [15] K. Yamaguchi, K. Yamada, S. Shoji, Y. Uno, H. Takeda, S. Toyooka and H. Tuboi, Simulation for nondestructive evaluations by magnetic sensor, IEEE Trans. Magn. 36 (2000),1710 1713 [16] K. Yamaguchi, K. Yamada and T. Takagi, Monte Carlo Simulation for Magnetic Materials including Dislocations, IEEE Trans. Magn. 38 (2002), 865 868 [17] K. Yamaguchi, S. Tanaka, H. Watanabe and T. Takagi, Monte Carlo Simulation for Barkhausen Noise, IEEE Trans. Magn. 40 (2004), 884 887 [18] K. Yamaguchi, S. Tanaka, O. Nittono, T. Takagi and K. Yamada, Monte Carlo simulation of dynamic magnetic processes for spin system with local defects, Physica B 343 (2004), 298 302 [19] K. Yamaguchi, S. Tanaka, O. Nittono, K. Yamada and T. Takagi, Monte Carlo Simulation of Barkhousen Noise for Micro Magnetic Clusters, IEEE Trans. Magn. 41 (2005), 1536 1539 [20] K. Yamaguchi, S. Tanaka, O. Nittono, K. Yamada and T. Takagi, Monte Carlo Simulation for Magnetic Dynamic Process of Deformed Micro Magnetic Clusters, IEEE Trans. Magn. 42 (2006), 927 930 [21] K. Yamaguchi, S. Tanaka, O. Nittono, K. Yamada and T. Takagi, Monte Carlo simulation for magnetic dynamic processes of micromagnetic clusters with local disorder, Physica B. 372 (2006), 251 255 [22] K. Yamaguchi, K. Suzuki, O. Nittono, T. Takagi and K. Yamada, Angle resolved analysis of magnetic hysteresis for micro magnetic clusters with local deformations, Physica B. 403 (2008), 354 359 [23] K. Yamaguchi, K. Suzuki, O. Nittono, K. Yamada, M. Enokizono and T. Takagi, Monte Carlo Simulation for Magnetic Domain Wall Displacements in Magnetic Nano Wires with Local Disorders, IEEE Trans. Magn. 45 (2009), 1622 1625

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-362

Metamaterials in electromagnetic nondestructive evaluation Adriana SAVIN, Rozina STEIGMANN, Alina BRUMA, Nicoleta IFTIMIE and Raimond GRIMBERG National Institute of Research and Development for Technical Physics, Iasi, Romania

Abstract. This paper proposes the study and implementation of metamaterials in the electromagnetic nondestructive examination; these materials can serve as electromagnetic flux concentrators in radiofrequency range. Thus, the using of a new type of metamaterials, namely conical Swiss roll has been proposed. As direct application, Carbon Fiber Reinforced Plastics (CFRP) plates with and without delaminations, created by impacts with low energy, were examined with the electromagnetic transducers with metamaterial lens. The characteristics of carbon fibers woven structure became visible and the delaminations are clearly emphasized. Keywords: metamaterials, nondestructive evaluation

conical

Swiss

roll,

CFRP,

electromagnetic

1. Introduction Basically, the nondestructive examination of a material consists in the applying a physical field to the object examined and evaluating the interaction between the field and the eventual material flaws. If the physical field applied to the examined object is an electromagnetic field with frequencies ranging from tens of hertz to tens of gigahertz or even terahertz, the procedure is named electromagnetic nondestructive examination. When the object to be examined has high electrical conductivity, and inhomogeneities (voids, inclusions, cracks - having lower electrical conductivity) are present in the interior, under the action of the electromagnetic field, eddy currents will be induced inside the object. The inhomogeneity will become a new current source within the structure of the tested object [1], [2]. If the electrical conductivity of the tested piece is lower then the one of the inhomogeneities (which is the case of carbon fiber reinforced plastics that present delaminations due to impact with different energies), the phenomenon that contributes to the detection of inhomogeneities is the electromagnetic field scattering on conductive zones by different shapes and positions inside the dielectric medium [3], [4]. As long as the frequencies used are not high (lower than 1GHz), the incident electromagnetic field is usually created by the coils circulated by alternative currents or current impulses. The detection of electromagnetic field created by the secondary current sources, or the detection of the scattered one, can be made either by coils or, in the case of low frequency field, specific sensors, i.e. sensors with Hall Effect or SQUID [5].

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To obtain more precise mapping of regions with electrical conductivities different from the ones of the host material, the assembly generation of electromagnetic field – detection should assure a spatial resolution as better as possible. In order to obtain a signal to noise ratio as large as possible at detection, leading to the increase of detection probability for a higher reliability coefficient, the use of a small lift-off (i.e. distance between the electromagnetic transducer and the controlled piece) is necessary [6]. This leads to the necessity of working in near field, as the generated and the scattered electromagnetic waves respectively are evanescent waves (i.e. waves that are rapidly attenuated with the distance [7]) and are difficult to be focalized using classical materials.

2. Conical Swiss roll as metamaterials Metamaterials [8] can provide an engineered response to electromagnetic radiation that is not available from the class of naturally occurring materials. They consist of individual or arrays of elements for which all the geometrical dimensions are small compared to the wavelength of operation. Because the wavelength of the electromagnetic radiation is large (at 300MHz, the wavelength in air, O0=1m), the condition that the element should be much smaller than wavelength is accomplished. A conical Swiss roll consists of a number of spiral-wound layers of insulated conductor on a conical mandrel, Figure 1.

a

b

Figure 1. Conical Swiss roll: a) Schematic of a conical Swiss roll; b) Photograph of a conical Swiss roll

The insulated conductor is a copper foil with 18μm thickness and a layer of polyamide with 12μm thickness (LONGLITETM200 produced by ROGERS CORPORATION USA). The Copper and polyamide layers have been laminated without adhesive to decrease the losses at high frequencies. The insulated layer has a relative dielectric permittivity of 3.2 and loss tangent, tanδ=0.0099. The conical Swiss rolls have 5 layers, 20mm base diameter, 3.2mm top diameter, the aperture angle 200 and height 55mm. Only few conical Swiss rolls with similar properties were selected from a produced range. Pendry et al. [8] proposed that Swiss roll made from thin conducting sheets have a macroscopic magnetic behaviour for a magnetic field applied along the rod. The radio frequency magnetic field will induce currents on the circumference of the cone (Figure 1a) and consequently a magnetization opposing the applied magnetic field. The capacitive and conductive elements of the structure create a resonant RLC circuit that the induced currents are subject to, and therefore a resonant P taking high positive and negative value for a range of frequencies is achieved [9]. Thus, a conical Swiss roll can act as radio frequency magnetic flux concentrator.

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To determine the effective magnetic permeability of a conical Swiss roll, the S parameters have been measured using a Network/Spectrum/Impedance Analyzer 4395A Agilent coupled with S Parameter Test Kit 87511A, Agilent, USA. The electromagnetic field is generated by a coil with 2 turns having 16mm diameter, made of 1mm diameter copper wire. The response of conical Swiss roll metamaterial is measured with a reception coil having 2 turns with 3mm diameter (Figure 2a). The dependence of real and imaginary components of S11 and S21 by the frequency is presented in Figures 2b and c.

a

b

c

Figure 2. Dependence of S paramaters by frequency: real component and imaginary component: a) experimental set up; b) S11; c) S21

According to [10] the impedance of the metamaterial considered a homogeneous slab and excited by a plane wave is given by

A. Savin et al. / Metamaterials in Electromagnetic Nondestructive Evaluation

Z

r

1  S11 2  S212

365

(1)

2 (1  S11 )2  S21

The sign in front of the square root sign is chosen such that

Re(Z ) t 0

(2)

The refraction index of metamaterial n, is obtained as solution of transcendental equation

e jnk0d

where

j

k0



1

2 2 2S21 1  S11  S21



r j 1



1

2 2 2S21 1  S11  S21



(3)

2S f with f - the frequency and c – the speed of light in vacuum, c

1 , d – the height of conical Swiss roll; the + or – sign is chosen such that Im(n) t 0

(4)

In these conditions the effective magnetic permeability of a conical Swiss roll is given by

Peff

Re(n) Im(Z )  Im(n) Re(Z )

(5)

where n is the refraction index, solution of eq. (3) and Z is the impedance of metamaterial given by eq. (1). In Figure 3 is presented the dependency of frequency for the effective magnetic permeability of a conical Swiss roll. It can be observed that the effective magnetic permeability became high for a certain frequency range, whereas for certain frequencies it became negative. As applications in the domain of electromagnetic nondestructive examination we are proposing an optimized work frequency of 72.5 MHz which assures a magnetic effective permeability of 22. At this frequency, the property of a conical Swiss roll as alternative magnetic flux concentrator has been verified. Using the Network/Spectrum/Impedance Analyzer 4395A Agilent, it has been measured the electromotive force (emf) induced in the detection coil that is displaced with a XY motorized stage Newmark type over the small basis of the conical Swiss roll at the distance of 1m. The dependence of the amplitude of the emf induced in the reception coil by the frequency is presented in Figure 4.

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Figure 3. Dependence by frequency of effective magnetic permeability of conical Swiss roll

Figure 4. The dependence of the amplitude of the emf induced in the reception coil at the scanning along the small base of the Swiss roll. Lift off 0.2mm

Examining data from Figure 4 it can be observed that in the zone corresponding to the diameter of the small base of conical Swiss roll, for a frequency that assures a maximum of effective magnetic permeability of the investigated metamaterial, the concentration of the radio frequency magnetic flux is very high. Also, it must be mentioned that on this aperture the magnetic flux is almost constant, fact that suggests the existence of an electromagnetic plane wave.

3. Near field images using conical Swiss roll Let consider a layout of two Swiss rolls disposed as in Figure 5. The small basis of the first Swiss roll behaves as a circular aperture and, due to radio frequency flux concentration properties, previous described, the “rays” that pass inside can be traced. Thus, the “object” plane is in the front of the aperture of Swiss roll I and the focal plane is located in the plane of small base of Swiss roll II. Into a region without sources, the Helmholtz wave equation is [3]

Figure 5. Layout of two conical Swiss rolls acting as lens to obtain near field images

’

2



 k 2 E  x, y, z 0

(6)

where k is the wave number k= 2S f , with f frequency and v the propagation speed of v the electromagnetic waves in the considered media. In angular representation, for a plane wave

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f f

³ ³ Ek  k x , k y e  2S f f 1

E  x, y , z



j kx xk y y

2

dk dk x y

(7)

where angular spectrum is



Ek k x , k y



f f

1

³ ³ E  x ', y ', 0 e  2S f f



 j kx xk y y

2

dx ' dy '

(8)

k 2 ! k x2  k y2 , the electromagnetic wave is a plane wave, and if

If

k 2  k x2  k y2 , the electromagnetic wave is an evanescent wave, being rapidly damped along z axis. If the evanescent waves are the dominant states, condition accomplished at distances smaller than the wavelength, the field in any z position will be

E  x, y , z

f f

³ ³   4S 2 f f 1

where



fk kx , k y e





jk x ¬ª x  j sign  k x  z  z0 ¼º  jk y ª y  j sign k y  z  z0 º ¬ ¼ dk

(9) x dk y



f k k x , k y is the angular spectrum of the field from aperture

­1 if sign  k x ® ¯0 if

­ °1 if ® ° ¯0 if

kx ! 0 ; sign k y kx  0



ky ! 0 ky  0

Considering a wave that has constant angular spectrum in aperture, truncating the integral from (9) at a double finite sum we obtain



f kx , k y



­ E0 ® ¯0

if

ka d k x d kb , ka d k y d kb

in

rest

(10)

Using the Fourier optics method [11] for the condition given by (10), the field in focal plane is obtained

E  x, y0  2d , z

E0

S2

k k · § k k j¨ b a x b a y ¸ 2 2 © ¹ e

§ k k sin ¨ b a © 2 x

· § k k x ¸ sin ¨ b a ¹ © 2 y

· y¸ ¹ (11)

A relatively uniform angular spectrum can be obtained by scattering an electromagnetic wave on a small scatter of circular shape made from a material considered a perfect electromagnetic conductor (PEC). The diameter of the focal spot of the metamaterial lens will be given by [11]

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D

4S kb  ka

(12)

and will be, according to Figure 5, equal with the diameter of the small basis of the conical Swiss roll (i.e 3.2mm). Inserting this value in (12), the values of kb and ka are obtained, and, the field in the focal plane can be calculated, according to (11).

4. Experimental results Plate from CFRP type having 6 layers of carbon fibers woven type 5 harness satin (Carbon T300 3K 5HS) with a layout that assures the quasi-isotropic properties of the plate were studied. The polymer matrix is made of Polyphenylene Sulphide (PPS). The thickness of the plate is 1.91mm with 0.5 volume ratio. The plates are produced by TenCate Advanced Composites, Netherlands. On these plates, delaminations due to impact with different energies have been induced using a spherical impactor with 22mm diameter. The plates were examined by means the electromagnetic procedure described above using the transducer presented in Figure 6, which contains a metamaterial lens, for detection. For the plane wave generation, a conical Swiss roll also has been used, acting as a flux concentrator. The lift-off was maintained constant at 0.25mm; the material to be examined can be considered practically in the plane of the aperture, the reception coil being in the focal plane of the lens. The control frequency was 72.5 MHz. In Figure 7, we present [12] the schematic layout of the 5H satin carbon fibers woven.

Figure 6. The electromagnetic transducer with metamaterials lens

Figure 7. Schematic representation of 5H biaxial woven fabric architectures

In Figure 8a is presented the amplitude of the signal delivered by the electromagnetic transducer with metamaterials at the scanning of a region of composite without delamination. The structure of CFRP obtained with the electromagnetic transducer with metamaterials respects with high fidelity the structure of the first layer of carbon woven 5H type.

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In Figure 8b is presented the signal given by the same transducer at the scanning of a region of composite which contains a delamination due to an impact with 2.5J energy. On the edges of the electromagnetic image, the structure of the woven can be observed; in the central zone, the delaminated region is emphasized.

a

b

Figure 8. The measured amplitude of the signal delivered by the electromagnetic transducer with metamaterials at the scanning of a CFRP zone: a) without delamination; b) with delamination

This zone becomes electromagnetically detectable due to the modification of the electrical conductivity on the normal direction to the woven plane as a consequence of the impact [13].

5. Conclusions The metamaterials have started to be intensely studied mainly in the last decade, both from a theoretical and experimental point of view. Using a new type of metamaterial – conical Swiss roll, a series of new type of applications such as electromagnetic examination procedures can be designed. These are mainly based in on the fact that the conical Swiss roll presents high effective magnetic permeability in the range of radio frequencies such that, due to their shapes, can serve as radio frequency magnetic flux concentrator. By coupling two conical Swiss rolls, lenses of metamaterials can be designed and studied using Fourier optics. The electromagnetic transducers based on lenses with metamaterials can be used with good results at the examination of small dimensions electrical conductive bodies embedded into the dielectric matrix. Clear images of the woven of carbon fibers from CFRP can be obtained and delamination due to impacts with low energies can be emphasized.

6. Acknowledgments This paper is partially supported by the Romanian Ministry of Education, Research and Innovation under Nucleus Program – 09 43 01 04 and National Plan II - Contract no. 71-016/2007- MODIS.

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7. References [1] C.V.Dood, W.E.Deeds, Analytical Solutions to eddy Current Probe Coil Problems, J Appl. Phys.., 39, pp. 2829 2838, 1968 [2] J.R.Bowler, Eddy current interaction with an ideal crack, Part I: The forward problem, J. Appl. Phys. 75(12) pp. 8128 8137, 1994 [3] J.Van Bladel, Electromagnetic fields, 2nd Ed., IEEE Press, 2007 [4] R.Grimberg, A.Savin, R.Steigmann, A.Bruma, P.Barsanescu, Ultrasound and eddy current data fusion for evaluation of carbon epoxy composite delaminations, INSIGHT, 51, (1), pp.25 32, 2009 [5] P.O.Moore, S.S.Udpa, Nondestructive Testing Handbook, 3rd Ed., Vol 5, Electromagnetic testing, ASNT, OH, 2004 [6] P.J.Shull, Nondestructive evaluation: Theory, techniques and application, Technology&Engineering, NY, 2002 [7] A.Grbic, G.V. Eleftheriades, Growing evanescent waves in negative refractive index transmission line media, APPLIED PHYSICS LETTERS, 82, (12), pp.1815 1817, 2003 [8] J.Pendry, A.J.Holden, D.J.Robbins, W.J.Stewart, Magnetism form conductors and enhanced nonlinear phenomena, IEEE Trans.Microw.Theory Tech., 47, pp. 2075, 1999 [9] M.C.K.Wiltshire, Radio frequency (RF) metamaterials, Phys.Stat.Sol.(b), 4, pp.1227 1236, 2007 [10] X.Chen, T.Grzegovczyk, B I.Wu, J.Pocheco, J.A.Kong, Robust method to retrieve the constitutive effective parameters of metamaterials, Phys.Review E,70, pp.1 7, 2004 [11] M.Born, E.Wolf, Principles of Optics, 7th Edition, Cambridge University Press, 2002 [12] R.Akkerman, Laminate mechanics for balanced woven fabrics, Composites:Part B, 37, pp.108 116, 2006 [13] R.Grimberg, D.Premel, A.Savin, Y.Le Bihan, D.Placko, Eddy current holography evaluation of delamination in carbon epoxy composites, INSIGHT, 43, (4), pp. 260 264, 2001

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Evaluation of Plastic Deformation in Steels by Magnetic Hysteresis Measurements Gábor VÉRTESY a,1 , Shuzo UEDAb, Tetsuya UCHIMOTOc, Toshiyuki TAKAGIc, Ivan TOMÁŠd and Zofia VÉRTESYa a Research Institute for Technical Physics and Materials Science, Budapest, Hungary b Japan Society of Maintenology, Tokyo, Japan c Institute of Fluid Science, Tohoku University, Sendai, Japan d Institute of Physics, Praha, Czech Republic

Abstract. Tensile tests of plastically deformed specimens were performed in order to investigate the relation between variation of magnetic characteristics and residual plastic strain. Deformed stainless steel (SUS316L) and carbon steel (SS400) specimens were investigated by the method of Magnetic Adaptive Testing, measuring and evaluating series of minor magnetic hysteresis loops. Reliable correlation was found between magnetic parameters and residual strain of the specimens. Magnetic descriptors also depend on the orientation of magnetizing field with respect to the direction of elongation. Based on these results, Magnetic Adaptive Testing is suggested as a highly promising non destructive method for monitoring plastic deformation in different types of steel. Keywords. Magnetic Adaptive Testing, Magnetic hysteresis measurements

1. Introduction Magnetic measurements are frequently used for characterization of changes in structure of ferromagnetic materials, because magnetization processes are closely related to microstructure of the materials. This fact also makes magnetic measurements an obvious candidate for non-destructive testing, for detection and characterization of any defects in materials and manufactured products made of such materials [1,2,3]. Structural non-magnetic properties of ferromagnetic materials have been nondestructively tested using traditional magnetic hysteresis measurement methods for a long time with fair success. A number of techniques have been suggested, developed and currently used in industry, see e.g. [4,5]. They are mostly based on detection of structural variations via the classical macroscopic parameters of hysteresis loops. An alternative, more sensitive and more experimentally friendly approach to this topic was considered recently in [6] and [7], based on magnetic minor loops measurement. In [6] the method of Magnetic Adaptive Testing (MAT) was presented, which introduced general magnetic descriptors to diverse variations in non-magnetic properties of ferromagnetic materials, optimally adapted to the just investigated property and 1

Corresponding Author. Gábor Vértesy, Hungarian Academy of Sciences, Research Institute for Technical Physics and Materials Science, H 1525 Budapest, P.O.Box 49, Hungary, E mail: [email protected].

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material. In [7] the sets of minor hysteresis loops were scrutinized, and sensitive descriptors of plastic deformation of the material (independent on the minor loop amplitudes) were identified. As another method, a hyperbolic model of magnetization was applied for describing the magnetization curves of magnetic alloys. This model provides an analytical solution to the complex phenomena of magnetic hysteresis [8]. Magnetic Adaptive Testing has already been successfully applied for investigation of structural changes in several different materials. For instance, cast iron material was measured [9], cold rolled low-carbon steel was studied [10] and also cold-rolled austenitic stainless steel samples were non-destructively characterized by this technique [11]. However, degradation of low-carbon steel and austenitic stainless steel with plastic tension after unloading has not still been investigated by MAT. Influence of plastic tension causes different structural changes in the specimen than cold rolling. The studying of this phenomena is extremely important for the inspection of nuclear power plants. The purpose of this work is to investigate the influence of plastic deformation in stainless steel (SUS316L) and in carbon steel (SS400) specimens by Magnetic Adaptive Testing. Furthermore, another novelty is this work is to study the influence of plastic deformation as a function of magnetizing field with respect to the direction of applied tensile stress.

2. Experimental Carbon steel SS400 and austenitic stainless steel SUS316L materials were used for the measurements. The specimens were made from 500x100 mm2 plate of 3 mm in thickness. The residual strain, ε, was added by tensile loads. Values of the residual strain for both types of materials are given in Table 1. Two specimens with each strain were measured. Maekawa universal testing machine was used at room temperature in air. The strain gage was located in the middle area of the specimens. The specimens can be seen in Fig. 1(a). The test equipment is shown in Fig. 1(b). The stress-strain diagram of the stainless steel sample is shown in Fig. 2. For magnetic measurements 100x70mm2 size pieces were cut from the strained plate. Table 1. Added residual strain for carbon steel (SS) and austenitic steel (SUS) samples Specimen SSRef1 SSRef2 SS2 SS4 SS5 SS7 SS8 SS10 SS11 SS13 SS14 SS16 SS17 SS19

Residual strain, ε [%] 0 0 0.2 0.2 0.5 0.5 1 1 2 2 5 5 10 10

Specimen SUS2 SUS4 SUS5 SUS7 SUS9 SUS10 SUS11 SUS12 SUS14 SUS15 SUS17 SUS18 SUS20 SUS22 SUS24 SUS25

Residual strain, ε[%] 0.2 0.2 0.5 0.5 1 1 2 2 5 5 10 10 20 20 50 50

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All samples in the two series were measured by the MAT method. Both directions of magnetization in parallel and perpendicular to the tension direction were examined. A specially designed Permeameter [12] with a magnetizing yoke was applied for measurement of families of minor loops of the magnetic circuit differential permeability. The magnetizing coil wound on the yoke gets a triangular waveform current with step-wise increasing amplitudes and with a fixed slope magnitude in all the triangles. This produces a triangular time-variation of the effective field in the magnetizing circuit and a signal is induced in the pick-up coil. As long as the field sweeps linearly with time, the voltage signal in the pick-up coil is proportional to the differential permeability of the magnetic circuit. The Permeameter works under full control of a PC computer, which registers data-files for each measured family of the minor “permeability” loops. The experimental raw data are processed by an evaluation program, which divides the originally continuous signal of each measured sample into a family of individual permeability loops and it is chosen for next processing. The program filters experimental noise and interpolates the experimental data into a regular square grid of elements, μij≡μ(hai,hbj), of a μ-matrix with a pre-selected field-step. Here (hai,hbj) are the field coordinates of the element, hai being the value of the sweeping field, and hbj amplitude of the minor loop. Each μij-element represents one “MATdescriptor” of the investigated material structure variation.

Figure 1. Appearance of the test specimens (a) and the test equipment (b).

5 00

2

σ [N/mm ]

4 00

3 00

2 00

1 00

0 0

2

4

6

8

10

12

14

ε appl [% ]

Figure 2. The stress strain diagram of the SUS sample.

The matrices are processed by another evaluation program, which normalizes them by a chosen reference matrix, and arranges all the mutually corresponding elements μij of all the evaluated μ-matrices into a μij(ε) table. Each μij(ε)-column of the table, i.e. variation of each MAT-descriptor with residual strain, numerically represents one “μij(ε)-degradation function” of the material. The consecutive series of μ-matrices,

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each taken for one sample with a value of the strain, εk=0%, 0.2%, 0.5%,... , of the consecutive series of the more-and-more deformed steel, describes the magnetic reflection of the material plastic deformation. Integrating the permeability along the field, ha, hysteresis loops and B-matrices can be obtained. The B-matrices contain in principle the same information as the μ–matrices, however, presentation of the ε-dependences is different and sometimes more advantageous.

3. Results

Induced signal (~permeability) [V]

In the case of carbon steel, definite differences were found in the directly measured signal (~permeability) of differently deformed samples, as shown in Fig. 3. However, in spite of large differences among the magnetic properties of the samples, there is no evident correlation between the permeability values and the given independent parameter, namely the residual strain. SS8

0 08

SSRef1

SSRef2

SS14 SS16 SS19 SS11 SS13 SS2

SS7 0 06

SS10 SS17

0 04

SS5 SS4

0 02

0 00 15

10

05

00

05

10

15

Magnetizing current [A]

Figure 3. Induced signals of the SS400 samples as functions of the magnetizing current. The plotted curves are proportional to the increasing hysteresis half loops.

Similarly, the calculated μij-degradation functions did not reveal systematic correlation with residual strain. On the other side, the optimal Bij-degradation functions show good correlation with ε, as plotted in Fig. 4. Here all the Bij values are normalized by one of the reference (SSRef1) not deformed) samples. Note, that significant difference was found if the direction of magnetization was taken parallel or perpendicular with respect to the direction of elongation. The most deformed samples had about 5 times larger MAT descriptors than the not deformed sample. 6 Parallel

Optimal Bij functions

5

4

3 Perpendicular 2

1 0

2

4

6

8

10

12

Residual strain, ε [%]

Figure 4. The optimal Bij(ε) degradation functions vs. residual strain of carbon steel for parallel and perpendicular magnetization with respect to the elongation.

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375

nduced signal (~permeability) [V]

The stainless steel samples are very weakly magnetic, in contrast to the carbon steel samples. It is difficult to perform any magnetic measurement on these samples. This character is very well reflected on the directly measured (permeability) curves, as shown in Fig. 5. 0,0074

0,0072

0,0070

SUS2 SUS17 SUS22 SUS25

0,0068

0,0066

-1,0

-0,5

0,0

0,5

1,0

Magnetizing current [A]

Figure 5. Induced signals of the SUS samples as functions of the magnetizing current. The plotted curves are proportional to the increasing hysteresis half loops. Only four samples are depicted, for the sake of legibility of the plot.

It is not surprising, that in this case of stainless steel also no correlation with the residual strain can be seen if the evaluated μ-degradation functions are considered. But similarly to the case of the carbon steel samples, good, definite and reproducible correlation was found between the derived Bij(ε)-degradation functions and the residual strain. Fig. 6 shows the correlation between the optimally chosen B-degradation functions and the residual strain, for the orientation of the magnetizing field being both parallel and perpendicular with the samples elongation. In this case all the values are normalized by the corresponding values of sample SUS4. Almost the same result was obtained, if sample SUS2 was used for normalization (not shown here). The low values of parameters, however, can sometimes cause a problem, if they are normalized with each other. To be sure, the calculation was also performed without normalization. It was found that the correlation is not affected by the way of normalization. 1,5

Optimal Bij functions

1,4

Parallel

1,3 1,2 1,1

Perpendicular

1,0 0,9 -10

0

10

20

30

40

50

60

Residual strain, ε [%]

Figure 6. The optimal Bij(ε) degradation functions vs. residual strain of stainless steel for parallel and perpendicular magnetization with respect to the elongation..

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In the perpendicular direction almost no influence of elongation was found on the MAT descriptors, but in the parallel case the optimally chosen magnetic parameter was about 30% larger as compared with the reference sample. The scatter of points is rather large, but the tendency is clearly seen.

4. Discussion As it is shown above, the magnetic minor hysteresis loop measurements, performed by a magnetizing yoke, after proper data evaluation, is suitable for detection of plastic deformation in the SS400 carbon steel and also in the SUS316L stainless steel, if the data are evaluated by the Magnetic Adaptive Testing method. In contrast to the previously observed case on cold rolled steels, the primarily measured permeability values (and also the μ-matrices) on tensile stressed samples do not seem to correlate with the material degradation, so they are not suitable to characterize the plastic deformation of the investigated samples. However, parameters, which describe the magnetic induction, B, and/or derivative of the permeability, μ’, (not shown in this paper) of the samples give well acceptable results. This experience demonstrates well the multiparametric behaviour of Magnetic Adaptive Testing. MAT is considered a way towards optimization of hysteresis testing, where those magnetic descriptors of the varied structural properties, are chosen, which are best adapted to the investigated property and to the investigated material. The scatter of points is relatively large, however, the tendency is clearly seen and the magnetic descriptors are reliable and reproducible as concluded from the repeated measurements on the same series of samples under different experimental conditions (different yokes, different speed of magnetization, etc.). Large difference between the characteristic values was found, if the samples were magnetized in the parallel or perpendicular directions with respect to the samples elongation. In case of perpendicular magnetization with respect to the elongation only very weak influence was found, while in case of paralallel magnetization the most degraded samples have about five times larges magnetic descriptors than the reference, not elongated sample has. This fact shows the anisotropic character of material degradation, and it also makes evident the capability of MAT to reveal this anisotropy. The well known and widely studied phenomenon, formation of Lueder bands in our carbon steel specimens has not been studied, because it is not the subject of the present work. Degradation of a low-carbon steel with plastic tension was investigated after unloading by magnetic methods (major hysteresis loop measurement and Barkhausen noise, BN emission) [13]. In this work magnetically closed samples (rings and frames) were measured. Monotonous correlation was found between ε and Hc and also between ε and BN. Due to 20% residual strain, coercivity increased by about 75%, while BN increased less than 10%. The behaviour of the hysteresis parameters and the RMS values of BN was explained by the change of the dislocation structure of the material with the deformation, which was confirmed by TEM observation. We received similar correlation between magnetic descriptors and strain, but in our case the sensitivity was much larger and we used magnetically open samples, which were magnetized by attaching a yoke. Our method can only be considered as really nondestructive one.

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Austenitic stainless steel was previosuly investigated by Magnetic Adaptive Testing, but in that case the conditions were quite different. In the case, described in [11], titanium stabilized austenitic stainless steel, 18/8 type, was studied where stripe-shaped specimens were cut from the original stainless steel plate. The specimens were annealed at 1100 °C for 1 hour. Then they were quenched in water in order to prevent any carbide precipitation, and to achieve homogeneous austenitic structure as the starting material structure. Then the as-prepared stainless steel specimens were coldrolled at room temperature up to about 60% strain. This process resulted a significant amount of the ferromagnetic phase, which was measured by a conventional portable ferrite tester equipment. The most deformed samples had 69 % bcc α′-martensite, which is highly ferromagnetic. The ferromagnetic character of the deformed sample can be seen in Fig. 7, where the signal registered for one family of minor loops

Pick-up coil signal [arb units]

0 06 0 04 0 02 0 00 -0 02 -0 04 -0 06 -1 5

-1 0

-0 5

00

05

10

15

Magnetizing current, I [A]

Figure 7. Induced signals of cold rolled austenitic stainless steel sample as functions of the magnetizing current. All the minor loops are shown [11].

(measured on sample having 69% α′-martensite) is shown, similarly to Figs. 3 and 5, but here all the minor loops are shown. It is evident from this graph, that the magnetic behaviour of the previously and presently studies samples are very different. In the present case tha samples were almost no ferromagnetic, the content of martensite phase was very low. This result demonstrates very well the capability of Magnetic Adaptive Testing. The measured signal in this case is very weak, due to the very low magnetization of the samples and there is almost no difference in the measured plots of differently deformed samples. However, in spite of this fact, after the data processing, a reliable correlation can be found between the residual strain and the magnetic descriptors. Successful magnetic measurements on this type of material are still not known from the literature. Another advantage (compared to traditional magnetic hysteresis methods) of the MAT method is that the magnetic saturation of the samples is not required. It is possible to apply a small simple yoke for both the magnetization and for the measurement of magnetically open samples. The method does not give absolute values of the traditional magnetic quantities, but evidently it is able to serve as a powerful tool for comparative measurements, and for detection of changes, which occur in structure of the inspected samples during their lifetime or during a period of their heavy-duty service.

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5. Conclusions In the present paper additional advantageous features of previously shown and discussed Magnetic Adaptive Testing method were shown. New results were presented on two different, but similarly tortured sample series. This work demonstrates again that MAT seems to be a good method for replacing destructive methods by nondestructive magnetic measurements. MAT offers a large choice of parameters. According to the investigated material’s behavior, those parameters, which describe the material degradation the best, should be chosen. For the successful application of the MAT method, first it is necessary to make comparative, traditional, destructive measurements on a series of samples, for “teaching” the MAT. This teaching procedure determines the optimum degradation function/s (i.e. the optimum calibration function), and the method of Magnetic Adaptive Testing is best adapted to the investigated task in this way. Then, this/these chosen optimum degradation functions will serve as sensitive parameters for practical measurements on unknown samples (of the same kind) to be investigated. The presented results are encouraging for future practical applications of MAT in nondestructive material evaluation.

Acknowledgements The work was supported by Hungarian Scientific Research Fund through project A08 CK 80173, by the Grant Agency of the Czech Republic through project No.101/09/1323, and by the Czech-Hungarian Bilateral Intergovernmental S&T Cooperation project. Authors express their thanks also to Japan Society of Maintenology and Tokyo Electric Power Company for preparing the samples.

References [1] M.J. Johnson, C.C.H.Lo, B.Zhu, H.Cao, D.C.Jiles, J. Nondestruct. Eval. 20 (2000), 11. [2] D.C. Jiles, Magnetic methods in nondestructive testing, K.H.J.Buschow et al., Ed., Encyclopedia of Materials Science and Technology, Elsevier Press, Oxford, (2001), 6021. [3] I. Mészáros, Materials Science Forum, 473-474 (2005), 231 236. [4] D.C. Jiles, NDT International, 21 (1988), 311 319. [5] J. Blitz, Electrical and magnetic methods of nondestructive testing,, Adam Hilger IOP Publishing, Ltd., Bristol, 1991. [6] I.Tomáš, J.Magn .Magn. Mater,. 268 (2004), 178 185. [7] S.Takahashi, L.Zhang, T.Ueda, J.Phys.: Condens.Matter, 15 (2003), 7997 8002. [8] J. Takacs, I. Mészáros, Physica B., 403 (2008), 3137 3140. [9] G. Vértesy, T. Uchimoto, I. Tomáš, T. Takagi, J. Magn. Magn. Mater,. 322 (2010) 3117 3121. [10] G. Vértesy, I. Tomáš, S. Takahashi, S. Kobayashi, Y. Kamada, H. Kikuchi, NDT & E INTERNATIONAL, 41 (2008) 252 257. [11] G. Vértesy, I. Tomáš, I. Mészáros, J. Magn. Magn. Mater., 310 (2007) 76 82 [12] I. Tomáš, O.Perevertov., in: JSAEM Studies in Applied Electromagnetics and Mechanics 9, ed. T. Takagi and M. Ueasaka, (IOS Press, Amsterdam, 2001), 5 15. [13] J. Pal’a, O. Stupakov, J. Bydzovsky, I. Tomáš, V. Novák, J. Magn. Magn. Mater,. 310 (2007) 57 62.

High Frequency Techniques and Others

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-381

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GPR for UXO recognition Raimond GRIMBERG, Adriana SAVIN, Nicoleta IFTIMIE, Sorin LEITOIU and Aurel ANDREESCU Nondestructive Testing Department, National Institute of Research and Development for Technical Physics, 47 D.Mangeron Blvd., 700050, Iasi, Romania

Abstract. Ground penetrating radar (GPR) has become at present an instrument widely used in different domains. This paper is based on the using of GPR for detection and characterization of unexploded ordnances (UXO). The obtained experimental data and some signal and image processing procedures are presented in order to make a correct evaluation of type of UXOs, caliber, dimensions and their location in the horizontally plan as well in depth. Keywords. GPR, UXO, signal and image processing, shape recognition

Introduction Ground Penetrating Radar (GPR) is a non-intrusive technique used to obtain information about the medium below the surface of the earth. The technique relies upon transmission of electromagnetic energy into the earth, and subsequent reflection of the energy at interfaces of differing dielectric permittivity. There are a wide range of domains that have used GPR such as archaeology, geology, civil engineering, and military applications. Current applications of GPR include but are not limited to detection of unexploded ordnance (UXO), buried landmines (anti-personnel and antitank), road layer thickness measurements, position of underground pipes and cables. To operate successfully GPR must achieve [1] an adequate signal to clutter ratio; an adequate signal to noise ratio; an adequate spatial resolution of the target and an adequate depth resolution of the target. Most GPR systems detect the backscattered signal from the target, although forward transmission methods are used in borehole tomography radar imaging [2]. When a down-looking antenna is scanned over a relatively small target, a characteristic hyperbolic arc appears in the time-domain data. However, a significant limitation of GPR in this application is that it can be very difficult for a non-expert user to extract information about the underground from the raw data.

1. GPR principles A block diagram of a generic GPR system is shown in Figure 1. The transmitter can provide an amplitude frequency or phase modulated waveform signal and the selection of the bandwidth, repetition rate or mean power will depend upon the path loss and

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target dimensions. The transmitting (Tx) and receiving (Rx) antennas will be usually identical and will be elected to meet the characteristics of the generated waveform.

Figure 1. Block diagram of a generic GPR system.

The majority of GPR systems uses an impulse time domain waveform and receives the reflected signal in a sampling receiver. The key of success of this method lies in proper pre-processing of the GPR data, which is a very important step before formal data analysis can begin. Models of the GPR situation range from a simple single frequency evaluation of path losses to complete 3D time domain descriptions of the GPR and its environment. Modeling techniques include single frequency models, time domain models, ray tracing, integral techniques and discrete element methods. The Finite Difference Time Domain (FDTD) technique has become one of the popular techniques [1, 3].

2. The equipment and the studied samples The GPR equipment is Utility Scan - Standard System - GSSI – USA, having a 400MHz antenna. On the front wheel of the GPR displacing system, an encoder is mounted assuring the determination of the position with 1mm precision. The sampling raster is 0.04ms, the quantization being made on 16bits. An experimental test site has been arranged on a terrain from which metallic objects (the detection was effectuated with GPR), civil engineering materials and big stones have been removed. In this test site, parallelepiped holes with 1x1x0.8m3 dimensions have been practiced, where different types of ammunition (without explosive material) were buried. The ammunitions studied are presented in Figure 2.

R. Grimberg et al. / GPR for UXO Recognition

383

Figure 2. The ammunition tested

After its introduction in the hole, this was tamped with soil which has been pressed. In Figure 3, there is presented the GPR equipment in the test site. The average value of dielectric permittivity of the soil was determined during the measurements, using standard procedures [4] as being 6. Each situation has been individually simulated using GPRMax2D, based on FTDT method [3].

Figure 3. The GPR system at the test site

3. Signal processing Figure 4 presents the scan #19 which represents the passing over a zone in which a Kargo projectile (122mm caliber, 780mm length) was buried in a horizontal position (a) and the result obtained by simulation (b). It can be observed that in the case of real measurements, the image is very noisy, containing, in addition, clutters. Using the specific technology of ultrasound examinations, the image form Figure 4a is a B-scan made from 55 raw data A-scan type.

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a

b

Figure 4. Scan of Kargo projectile: a) raw data; b) simulation using GPRMAX 2D.

3.1. A-scan processing An important process operation is to ensure that the mean value of the A-scan be near to zero. This assumes that the amplitude probability distribution of the A-scan is symmetric about the mean value.

A 'n = An −

1 N

N

¦A n =1

n

(1)

where An -unprocessed data sample, A’n - processed data sample, n – the sample number, N – total number of samples. The next step in GPR signal processing is noise reduction and this can be achieved by either averaging each individual sample at the A-scan. The general effect is to reduce the variance of the white noise and gives an improvement in signal to noise ratio. The general form of the filtering operation is given by

A 'n = An +

An − A 'n −1 K

(2)

where A’n is the averaged value, An is the current value. The factor K may be chosen to be related to n, N, or a fixed value, which will weight the averaged value appropriately. Averaging has no effect on clutter. 3.2. B-scan processing If we consider an assembly set of five samples comprising a B-scan, there are a number of approaches to signal processing which can be considered. Imaging with GPR data is frequently hampered by clutter. The principal problem for a correct interpretation of GPR images consists in the extraction of unwanted signals as the ones due to transmission of the forward wave

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385

from Tx to Tr and those due to reflection on the air-soil interface. This operation is named background removal, a series of specific algorithms being used. The results, good enough, have been obtained using the simple procedure named subtract mean trace [5]. In this method, we define a window of L pixels and subtract the mean of the pixels from all the pixels in this window. The window is moved along and the procedure is repeated until the entire image is covered, as following i=

L

1 2 g ( x, y ) = f ( x, y ) − ¦ f ( x + i, y ) L i =− L

(3)

2

where g – filtered image, f- raw data and L is the window size. This method works well, even with GPR data taken over soil having an uneven profile, provided the magnitude of the ground reflection is uniform across the GPR map. Because of the factors such as variations in soil moisture content, vegetation, soil profile, etc, the method of subtract mean trace is often unsatisfactory in practice. We propose a method in which spatial variations in both the ground reflection magnitude and delay are simultaneously estimated using nonlinear optimization. Because these variations are relatively smooth functions of position, we model them using low-order polynomials. To proceed, the measured data are split into Nseg spatial segments. Over each segment we approximate the spatial resolution in both the amplitude and time delay of the ground reflection by weighted sums of Chebyshev polynomials, the domain of the segment was normalized to the interval [-1,1]. Let Ai(x) denote the spatially ground reflection amplitude and Bi(x) the time delay of the ground reflection peak over segment ith. We approximate Ai(x) and Bi(x) as a sum 4

Ai ( x ) = ¦ ain Tn ( x ) n=0

(4)

4

Bi ( x ) = ¦ bin Tn ( x ) n =0

where Tn(x) are the Chebyshev polynomials defined by the recursive relation

Tn +1 ( x ) = 2Tn ( x ) − Tn −1 ( x ) ,

n >1

(5)

with T0(x)=1 and T1(x)=x. Because the reflection coefficient at the air-soil interface is typically complex, we can represent the coefficients as

ai = ª¬ aireal , aiimag , aireal , aiimag , ...º¼ 0 0 1 1

(6)

bi = ª¬bi0 , bi1 , ...º¼

(7)

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The frequency-domain ground reflection in spatial segment ith can be estimated as

Giest ( x, f ) = Ai ( x ) H ( f ) exp ( −2π jfBi ( x ) )

(8)

where H ( f ) is the windowed frequency response of the radar, i.e.

H ( f ) = H ( f )W ( f )

(9)

In which H ( f ) is the average frequency spectrum of the raw GPR data within the

segment and W ( f ) is a window applied when creating the time-domain data. We have used a Hanning window. The time domain reflection estimated becomes

(

)

giest x, t , ai , bi = Ai ( x ) h ( t − Bi ( x ) )

(10)

where h(t) is the inverse Fourier transform of H ( f ) . The measured ground reflection over segment ith can be expressed as

(

)

gimeas ( x, t ) = giest x, t , ai , bi + ni ( x, t )

(11)

where ni(x,t) represents the modeling error. The coefficients ai and bi are found by a least-square error process, which requires a nonlinear optimization of

(

(

ª aˆi , bˆi º = arg min gimeas ( x, t ) − giest x, t , ai , bi ¬ ¼

)

2

)

(12)

Once the weighting coefficients ai and bi are estimated, the amplitude term Ai(x) and the delay Bi(x) of segment ith are evaluated using Eq. (4). The parameter estimation was performed using a nonlinear least square error minimization function, in the Matlab 2009b Optimization Toolbox. If the optimization routine does not converge for a data set, we must use a recursive approach. Imaging techniques can be used to focus the energy present in a point target’s hyperbolic arc back to a single point. This technique, named migration allows the determination of the depths of buried objects.

4. Results The GPR raw data for different types of UXO, presented in Figure 2, have been obtained. All types of UXO have been buried at 0.8m depth, excepting the antitank plastic mine that was buried at 0.6m, according to its indications for using it.

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Also, groups of different types of UXO have been used. The measurement conditions remained the same in all cases: 0.05m distance between row data in A-scan, 1024 samples/cm, 0.1m distance between successive B-scans, 20dB amplification. The signal processing methods and their efficacy are presented in Figure 5, corresponding to the scan #19 from Figure 4, including the procedures of A-scan processing described in chapter 3.1. In Figure 5a it is presented the background removal effect applied to the original image from Figure 4a.

a

b

c Figure 5. GPR images of kargo projectile: a) after A scan processing and ground removal; b) after migration; c) top view.

After applying migration technique, the region of maximum concentration of energy, corresponding to the real position of top surface of the kargo projectile has been emphasized. It can be observed that the migration procedure locates correct the superior part of the projectile. Concatening the B-scan obtained after migration of corresponding GPR images of the kargo projectile and applying top view technique, the image of the kargo is obtained and from simple measurements, the type and the dimensions of the projectile can be determined. Also, the depth at which the projectile has been buried can be determined from raw data after migration. The same techniques have been used for detection and evaluation of two projectiles, type 76mm caliber, the distance between their generatrix being 0.6m, Figure 6a. In Figure 6b there is presented the top view for an antitank mine MAT 62B. It must be mentioned that its shell is made from plastic, the metallic parts having a total weight of 15.8g.

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a

b

Figure 6. Top view: a) two projectile, 76mm caliber; b) antitank mine

5. Conclusions GPR has started to be used, with good results, in different types of application, from which, UXO must be mentioned. This fact is more important for the countries that have been theatre of war. To interpret correct the images delivered by GPR, due to the high level of noise and of clutters, it is very important to solve the forward problem using FDTD procedure. Applying specific procedures of signal and image processing, the shape of UXO become visible, the type, caliber, number and their coordinates can be determined from simple measurements on the results. These procedures allow to detect antitank mines from plastic, even if the weight of metallic parts is very small.

6. Acknowledgements Special thanks to the Colonel Stefan Lazar, Chief Inspector of Inspectorate for Emergency Situations “Mihail Grigore Sturdza” Iasi, Romania. This paper is partially supported by the Romanian Ministry of Education, Research, Youth and Sports under National Plan II Contract no.32 134/2008 SysArr.

References [1] D.J.Daniels, Ground Penetrating Radar, 2nd ed., , IEE 2004, UK. [2] M.J.g Yi, J.H. Kim, S.J.Cho, M. Sato, Integrated Application of Borehole Radar Reflection and Resistivity Tomography to Delineate Fracturesat a Granite Quarry, Subsurface Sensing Technologies and Applications, Vol. 6, No. 1, January 2005 [3] A.Giannopoulos “GprMax2D/3D, User's Guide”, 2003 [4] ISO11265:1994 Soil quality, Determination of specific electrical conductivity [5] C.C.Chen, J.D.Young, L.Peters, F.Paynter, Radar signature measurements of buried, unexploded ordnance targets, Tech.Rep. 727388 2, The Ohio State University, Electroscience Laboratory, Columbus, Ohio, 1994.

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-389

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Application of Microwave Interferometry in Complex Engineered Dielectric Materials Karl SCHMIDT, Jack LITTLE Evisive, Inc., 8867 Highland Road, #378, Baton Rouge, Louisiana, 70808 USA

Abstract. A portable microwave interferometry system has been demonstrated to detect material properties in high performance materials including engineered ceramics, organic and ceramic composites and other composite dielectric materials. The technique detects and images internal cracks, internal laminar features such as disbonds and variations in material properties such as density. It requires access to only one surface, and no coupling medium. Other NDE methods and destructive examination are used to verify performance. Keywords: Microwave Interferometry, NDT, Dielectric

Introduction A portable microwave interferometry system using the Evisive Scan™ microwave interference scanning method has been demonstrated to detect defects, material anomalies and material properties in high performance materials including engineered ceramics, organic and ceramic composites and other composite dielectric materials. This includes detection of defects and damage in composite ceramic armor; aerospace ceramic matrix composite material; fiber reinforced resin pipe, nuclear power plant flexible couplings and other high performance dielectric materials. The microwave interference scanning technique detects and images internal cracks, internal laminar features such as disbonds and variations in material properties such as density. It requires access to only one surface, and no coupling medium. Other NDE methods, including through-transmission x-ray, x-ray Computed Tomography, and destructive examination, are used to verify defects and other detected anomalies. The microwave-based method, having US and international patents, has been developed and demonstrated to be applicable to dielectric materials in a wide range of high value components.1 A probe (transmitter and receiver antenna) is moved over the part, bathing it in microwave energy. Some energy is reflected and transmitted at every interface of changing dielectric constant in the field of the transmitter. This includes the front and back surfaces of the part, and every “feature” in the part that has a discontinuity in dielectric properties. A microwave interference pattern is created when the reflected energy is combined with the transmitted signal to create the measured voltage at each position on the object. The Evisive Scan™ system has been advanced from laboratory demonstration to successful field applications. The microwave interference scanning technique has been applied in operating nuclear power plants for condition assessment of reinforced rubber

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flexible couplings.4 This work was qualified and applied under an NQA-1 compliant quality assurance program and is a basis for fleet-wide condition based maintenance program. Other applications are summarized. These include fiber reinforced resin composite structures and spiral wrapped pipe; pipe wrap repairs of steel pipe; and joints in high density polyethylene pipe.

1. Description of the Technology and Method The basic operating principle of this technology is based on the backscattering of microwaves as they travel from one media to another media with different dielectric constant. So a defect in the nonmetallic pipe is viewed as a new media with a different dielectric constant from the surrounding material. Hence it scatters the microwaves at a different rate and phase from the surrounding medium. The microwave energy applied in the method has wave lengths in the centimeter range and frequencies from 0.3 to 300 GHz. The images represent the reflected microwave energy from the entire volume of inspected material. The microwave energy transmits through gaps and material variations, and is reflected entirely by a conductive surface. This permits examination from one surface, without coupling media, through non contacting layers and coatings. Evisive Scan method requires access to only one side of a part. The microwave interference pattern is created by bathing the part in microwave energy as illustrated in Figure 1. The probe (transmitter and receiver antenna) is moved over the part, bathing it in microwave energy. Some energy is reflected and transmitted at every interface of changing dielectric constant in the field of the transmitter. This includes the front and back surfaces of the part, and every “feature” in the part that has a discontinuity in dielectric properties. A microwave interference pattern is created when the reflected energy is combined with the transmitted signal to create the measured detector voltage at each of the receivers. The voltage values for both receivers are saved with the associated X-Y position on the object.

Figure 1. Schematic diagram showing relative position of microwave transmitter and receiver head to the part under examination. One sided access is shown.

The microwave frequency used in the tests yields wavelengths in air of about 12.4 mm (0.49 inches) to 28.5 mm (1.12 inches). The magnitude of the phase difference between the emitted energy and reflected energy determines the voltage of the signal at the receiver. Hardware Channels A and B are separated by a quarter wavelength (¬/4) in the wave propagation dimension, Z. In any “image” data, the rate of change of the

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detected signal value impacts the “clarity” of that image. This relationship is illustrated in Figure 2. The amplitude repsonse of a feature is optimized at a Z dimension associated with maximum rate of change of the signal in the Z dimension. This is achieved for each channel by moving the emitter (and receiver) within a quarter wave length in the Z direction. This position is referred to as the “Stand-Off” distance. This is also affected by the frquency of the microwave signal, and can be adjusted in large (10 or 24 GHz) of fine increments.

Figure 2. The phase relationship of the receiver Channels presented as a theoretical standing wave, showing the phase relationship of a reflective surface

The reflected signal and transmitted signal form an interference pattern which is sampled over the surface of the part as illustrated in Figure 3. The image of a point reflector as shown in the diagram in Figure 3 is theoretically presented in Figure 4, in which this interference pattern is predicted mathematically for a point reflector.

Figure 3. The interference scan image is created by moving the probe over the surface of the part and sampling the interference pattern voltages.

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The image of features in the examined part is created by the interference pattern of reflections from the features and the transmitted signal. Thus, minimum detectable feature size can be much smaller than the wavelength. The magnitude of the phase difference between the emitted signal and reflected signal determines the voltage of the signal.

Figure 4. Mathematical plot of theoretical interference pattern from a point reflector

The anticipated interference pattern for a point reflector is illustrated in Figure 5, which shows Channel A and Channel B images for a small spherical reflector. Hardware Channels A and B are separated by a quarter wavelength (¬/4) in the wave propagation dimension, Z.

Figure 5. Channel A and Channel B images of a 2.54mm (0.10 inch) conductive sphere located 19 mm below the surface of a glass plate.

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2. Equipment Configuration The portable version of the Evisive Scan equipment is shown in Figure 6a. This shows the laptop-computer with the driving electronics and the scan head. The same computer and electronics can be coupled in the laboratory to an XY Positioning Table as shown in Figure 6b. Operating, interface and display software resides on the interface and display computer. Data are collected via an X-Y raster scan over the surface of the part.

Figure 6.

Photographs of portable scanning microwave system a

computer, electronics and head

A number of portable configurations have been applied to field use: The instrument and control system has been interfaced to mechanized pipe scanners and with a multi-axis position system for free-form manual positioning, and with a variety of manual position encoders. A portable system has been interfaced to an infrared camera as shown in the field in Figure 7.

Figure 7. Portable Evisive Scan equipment configured with infrared position tracking

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For free-hand positioning, the probe is manipulated manually, position tracked and presented in real-time. The tracking display facilitates control of coverage and scan density. Before and after images are automatically saved with each scan (the position tracking display is shown in Figure 8). The data rate is sufficiently high to assure that mechanical positioning or position feedback for manual positioning is the only limitation in scan speed. The scan data are available in near real time. Scan speed with the hand held infrared tracking system varies and may exceed 10 inches per second

a. Initial scan area display

b. Scan area with position trace

Figure 8. Scan area image and position tracking image (data points shown in green)

Evisive has incorporated the system electronics into the hand held probe housing and developed a wireless interface of the probe and control computer. This significantly reduces the system size, as well as improving field applicability. The Wireless Hand Held Evisive Scan system is shown in Figure 9.

Figure 9. Evisive Scan Wireless Handheld System. The Evisive Scan electronics and controls have been incorporated into the Probe Assembly, which communicates by Bluetooth with the User Interface Computer. The camera tracks the infrared beacon providing real time position and data input.

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3. Applications Experience The Evisive Scan™ technique has been successfully applied to complex engineered dielectric materials which present challenges to alternative non-destructive testing methods because of the complex structure of the material, or the subtle nature of the targeted defect. The following examples illustrate several of those applications.

3.1. Detection of Cracked Armor Tile and Delaminations in Assembled Part The Evisive Scan system has been demonstrated to detect cracked ceramic armor tile in a typical ceramic armor layered configuration. Figure 10 shows a correlation between a photograph of the part surface, a microwave scan image of the cracked tile and a through-transmission x-ray image of the same tile. The wide, light gray patterns shown in the microwave image follow the crack centerlines, which are hilighted in red. The Evisive Scan data has sufficient dynamic range, (greater than 12 bit resolution), to identify the centerlines and edges of features within the data position precision. The artificial cracking was created by compression with a drill press, crushing the ceter

Figure 10. Photograph (left), microwave interference scan image (center) and x ray image (right) of an artificially cracked tile in an armor panel.

region from which the cracks radiate. The tile is part of an actual armor panel which was also used for other destructive testing. The panel presented in Figure 11 has six artificial laminar features, arranged at two depths: above and below an elastomeric layer. The artificial features range in size from 6.4mm (0.25 inches) to 63.5mm (2.50 inches) square. Figure 11 shows that the scanning microwave system detected all six artificial laminar features. Similar artificial features were detected below (left in the image) and above (right in the image) the elastomeric layer in the part. The difference in geometry of the left and right presentation of these features relates to contours of layers above the deeper features which are on the left in the image. The difference in depth of the features is indicated by the difference in gray scale (voltage) which relates to their relative phase positions. The phase position of laminar features can be adjusted to “focus” the acquired image data at specific depths in the material, or to minimize the effect of specific laminar features. This is particularly beneficial in optimizing the technique for detection of laminar features at a specific layer in the complex material structure.

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The small circular indication in the upper right is apparently an unintended laminar feature near the depth of the artificial feature. The difference in depth of the artificial laminar features on the left side (underneath the rubber layer) and those on right side (above the rubber layer) is apparent in the dark (low negative voltage) and light (high positive voltage) phase difference associated with their depths. The consistent voltage of the three artificial laminar features on the left and right sides similarly indicates their common depth in the material. The circular indication at (9.5, 12.5) is from a laminar feature at a depth very near the artificial feature. The effect of the interaction with the elastomeric layer above the artificial features on the left is very clear in this image, with the edges of the features occurring at the center of the surrounding patterns.

Figure 11. Scanning microwave image data of specially prepared test sample prepared with artificial delaminations. Six different delaminations in three sizes, located at two depths were inserted and as noted here these were all detected.

The artificial feature and analogous feature at (9.5, 12.5) were examined by through transmission x-ray and x-ray computed tomography (CT). The anomalous laminar feature is also demonstrated to have a through wall dimension less than the minimum resolution of the CT image (smaller than about 0.25 mm).

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3.2. Clock Spring Inspection Inspection of the metal surface under a clock spring repair is another important application for microwave NDT. A clock spring repair is a composite reinforcement of carbon steel pipes to repair a leak or a corrosion pit by wrapping layers of composite material held together with epoxy. The surface of the metal is prepared using sand blasting and then the epoxy and composite wrap are applied and wrapped around the surface (usually 8 wraps) in a manual process. This repair is common in the oil and gas industry. If there is a void between the wrap and the metal surface due to poor workmanship then the corrosion process will resume. The microwave interferometry system has been successfully applied with a pipe scanner to inspect the volume of the clock spring and the metal surface under such a repair. An example of a test clock spring with artificial and natural defects is shown in Figures 12 and 13.

Figure 12. Clock Spring specimen. Fiber reinforced resin over wrap with interlayer mastic applied to a carbon steel pipe

Figure 13. Evisive Scan image of Clock Spring repair, showing artificial and natural features in the Clock Spring volume and in the carbon steel pipe surface.

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3.3 Large Tire Application The microwave interference scanning technique has been successfully applied to inspection of larger tires for detection of embedded stones. The stones enter the rubber tire tread under load, and migrate toward the steel reinforcing belts in the tire. If unchecked, they can wear against the reinforcing belt causing tire failure. The selected region is scanned freehand, using infrared position tracking. The scan coverage is shown in real time as presented in Figure 8. Embedded rocks are discriminated from cavity in the rubber tread and other anomalies by differentiating between the responses at different phase angles using Channel A and Channel B which are ¬/4 apart. In Figure 14, the deeply embedded stones appear as red in Channel A, and are diminished in Channel B, while the residue and open fissure appear as yellow and red in both Channels.

Figure 14. Channel A and B Evisive Scan images of stones in a large tire tread. The presence of red stone response in the Channel A (left) image only, indicates a stone deep in the crack.

In a field demonstration, local operators were trained in the differentiation technique, and performed at better than 90/90 detection / confidence percentage after eight weeks.

3.4. Application for Inspection of High Density Polyethylene Pipe High density polyethylene (HDPE) is used in a wide range of petroleum and power industry applications. Thermal fusion of pipe ends is commonly used to join pipe sections. Evisive licensee Exova, of Broxburn, UK, have applied the method thermal fusion joints, and have completed a number of destructive examinations to validate the application. The microwave interferometry method has been applied to HDPE weld joints in laboratory and field programs. In the specimen shown in Figure 15, a portion of the prepared weld surface was contaminated with talcum powder. The microwave interference scanning image displays the irregular pattern from the contaminated region of the weld which can be

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contrasted with the appearance of the properly formed weld in the pseudo-color scan image. The improper formation lacks the well-formed center response (dark blue to red in this image). In the image, the weld centerline is displayed at X=4.1 inches, and the circumference of the pipe is expressed in inches on the Y axis. The bend samples from the contaminated region and clean region of the weld provide confirmation of expected results: the contaminated region failed by brittle fracture and the successfully welded segment failed ductility.

Figure 15. Microwave interference scan image of a thermally fused butt joint which is contaminated with talc powder on part of the weld face. The uneven formation of a weld joint is evident at 1, and yields brittle failure in a bend test. The even formation of the weld is apparent at 2, and yields the desired ductile failure in the bend test.

3.5. Application in Ceramic Matrix Composites The Evisive Scan™ interferometry method has been successfully applied to metrology and non-destructive testing in ceramic matrix composite (CMC) materials. The material is formed with multiple layers of ceramic fiber fabric surrounded by a ceramic matrix. The complex structure of CMC materials, and the mechanical properties of the constituent materials present challenges to conventional non-destructive testing techniques. These properties lend themselves to inspection by microwave Interferometry. The series of images in Figure 16 includes a photograph of the sample part, and Evisive Scan™ images at two phase angles which correspond to different focal plane depths in the part. The part has three artificially created cavities which are clearly apparent in the images. The difference in display of the cavities in the two images illustrates the variation in geometry at the different depths. The feature on the right

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vividly shows the displacement of the material, which occurred during formation. Anomalies are apparent in all three features.

Figure 16. Top down: photograph, Channel A image and Channel B image showing differences in internal features at different depths in the CMC sample.

4. Summary The Evisive Scan™ microwave interferometry system has been developed and tested on a wide range of engineered dielectric materials. These include ceramic composite armor, composite matrix ceramic aircraft components, fiber reinforced resin components, high density polyethylene and rubber components. Applications include laboratory testing and field services projects. The method is applicable to material which is a bulk dielectric, requires access to one surface only and requires no coupling medium. Experiments with antenna configuration and post processing software

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demonstrate the ability to shape the beam pattern, and increase feature discrimination in complex materials.

Acknowledgements Work included in the report is supported by the US Air Force Research Laboratory, US Army Tank-Automotive Research, Development and Engineering Center (TARDEC), US Army Research Laboratory and US Air Force Research Laboratory. Evisive would also like to acknowledge project participation and support by Argonne National Laboratory, Saudi Aramco and Exova.

References [1] [2]

[3]

[4]

J. Salem, D. Zhu, Edited by L. Prokurat Franks, “Advances in Ceramic Armor III”, Ceramic Engineering and Science Proceedings, Vol. 28, Issue 5, 2007 K. Schmidt, J, Little, W. Ellingson, “A Portable Microwave Scanning Technique for Nondestructive Testing of Multilayered Dielectric Materials”, Proceedings of the 32nd International Conference & Exposition on Advanced Ceramics and Composites, 2008 K. Schmidt, J, Little, W. Ellingson, W. Green, “Optimizing a Portable Microwave Interference Scanning System for Nondestructive Testing of Multi Layered Dielectric Materials”, Review of Progress in Quantitative NDE, 2009 Bob Stakenborghs, Jack Little, Microwave based NDE Inspection of HDPE Pipe Welds, Proceedings of the 17th International Conference on Nuclear Engineering (ICONE17), July 12 16, 2009, Brussels, Belgium

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Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-402

Detection of Concealed, Graphite Containing Frescos, Using Microwave Enhanced Infrared Thermography Paweł LESIECKI a and Barbara SZYMANIK a1 Department of Electrical and Computer Engineering, Faculty of Electrical Engineering, West Pomeranian University of Technology, al. Piastów 17, 70-310 Szczecin, Poland a

Abstract. Active infrared thermography is one of the most popular NDT techniques. In this method an external energy source is used to produce the temperature difference between the feature of interest in examined specimen and the background. Thermovision cameras are used do observe obtained temperature differences. The variety of external energy sources can be used in IR thermography. Conventional sources (such as powerful halogen lamps or infrared heaters), apply heat externally to the surface of the material. The microwave irradiation, unlike to mentioned previously sources, penetrates and simultaneously heat the bulk of the specimen. For that reason, microwave heating can effectively minimize the heating times. This paper presents the method of detection of concealed graphite containing frescoes, using active infrared thermography with microwave irradiation as a heat source. It has be determined, that most of mural paintings, like frescoes, consist some amount of coal (in the form of carbon black used as a paint or charcoal used by the artist for sketching). Analysis of dielectric properties of coal shows that generally it can be considered as a good microwave absorber, therefore the high temperature difference between coal containing frescoes and the background is produced during the microwave heating of painting. Keywords. Microwave heating, concealed frescos detection, active thermography

Introduction According to report [1] most of the cultural heritage in Europe consist of buildings of historical meaning. There are many circumstances that affect the stability and the state of such constructions. Current assessment techniques of many historical buildings are based on optical inspection and laboratory measurements on samples taken. Such approaches are often not accurate or they may be harmful or even destructive for valuable works of art. There exist many modern NDT methods to determine the state of such structures. The most frequently methods applied are: Radar, impulse thermography, pulse-phase thermography, infrared thermography, geoelectric and microseismic methods. These methods can be used for inspection of known, well documented places for continuous maintenance but they can be used also for discovering previously unknown structures. In the mentioned report these techniques were used for revealing hidden doors which was walled up and plastered. In [2] and [3], 1

e-mail: [email protected]

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active thermography was used for studies of plastered mosaics. Especially radar and active thermography seem to be both fast and accurate methods for such inspections. Active thermography methods utilize external heat sources for object excitation and the temperature profile is recorded. Especially Impulse Thermography and its derivative – pulse phase thermography proved to be reliable methods in nondestructive testing. Impulse thermography is well known in many industrial applications as a tool for the detections of detachments, disbonds and voids. In building inspections passive thermography was used for many years mostly for testing thermal insulation quality. Since modern infrared cameras are very sensitive and offer good SNR, such investigations are fast and reliable tool for building assessment. As an extension to this, active thermography was successfully applied for locating defects like disbonds of tiles and plaster or honeycombing in concrete. In the above methods excitation and response were of the same nature and more or less in the same frequency band. Here we would like to introduce another approach that was studied earlier [4]. This approach uses excitation of one kind and processes response of another kind (or from another frequency). Such hybrid solution can take advantages from both. Here we would like to show an example of discovering hidden frescoes. We will make use of excitation in microwave band and response in infrared band.

1. Theory of microwave enhanced infrared thermography 1.1. Theory of microwave heating of graphite and plaster materials Microwave heating is mostly based on interaction between the electromagnetic field and the material at the molecular level [6]. Therefore the material's dielectric properties ultimately determine the effectiveness of such a heating. Microwave energy utilization is widespread and has been studied by many researchers [7]. This paper presents the method of detection the concealed, graphite containing frescoes, using active infrared thermography with microwave irradiation as a heat source. It has been determined [8], that most of mural paintings, like frescoes, consist some amount of coal (in the form of carbon black - used as a paint or charcoal used by the artist for sketching). Analysis of dielectric properties of coal [9] shows that generally it can be considered as a good microwave absorber, therefore the high temperature difference between coal containing frescoes and the background is produced during the microwave heating of painting. There are two physical mechanisms that sustain efficient energy transfer during microwave irradiation into non metallic material. At the lower end of the microwaves’ band conductive currents are flowing within the material. These currents that appear due to ionic conduction, can transfer energy from microwave field to the material. At higher microwave frequencies energy absorption is mainly due to the existence of permanent dipole molecules which try to re-orientate under the existence of the changing electric field. This loss mechanism has its origin in the inability of the polarization to follow the fast changing electric field. In the complex plane the polarization phasor lags the applied electric field component of the wave. This causes that resulting current has a component in phase with the applied field (a real part appears) and power is dissipated in the dielectric material. Summing up, the losses of a material can be expressed as a function of both dielectric loss and conductivity:

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ε r'' = ε rd'' +

σ ωε 0

(1)

The dielectric loss is characterized by the relative loss factor εr’’ which is part of the relative permittivity εr*=εr’+jεr’’ while absolute permittivity is given by ε=ε0ε*. The ratio tan δ =

ε '' ε'

(2)

is the dielectric loss tangent and it is frequency dependent. It describes how good a material absorbs microwave energy. In the absence of radiant heat losses and convection losses, for homogenous material we may easily express EM wave to thermal energy conversion process: Power density dissipated per unit volume is given as: P = ωε 0 ε '' E 2

(3)

were P – power density absorbed, f – frequency, E – electric field strength. Because of the relationship between conductivity and loss factor given above, we may write:

dT σE 2 = dt ρC p

(4)

It would appear that it is good to have greater conductivity to get greater energy conversion efficiency. However increased conductivity (or loss factor) has its drawbacks because of skin depth defined as the inverse of the attenuation factor: § ε ' · ºº ω ª ε ' ª« α= « 1 + ¨¨ '' ¸¸ − 1» » c « 2ε 0 « © ε ¹ »» ¬

¬

1/ 2

(5)

¼¼

Skin depth is the distance that wave reaches, before its E field component value drops to 1/e the value at the surface. In general we may classify material as either: transparent, reflective or absorbing. From both theoretical and experimental results we may see that insulator - type minerals and compounds are not good microwave absorbers and we may classify them as microwave transparent. All of the high conductivity minerals and compounds should be classified as microwave reflective materials since energy loss due to reflection is high and penetration depth is low. To detect plaster-covered frescoes we definitely need absorption difference between wall material and fresco paintings. Fresco painting material should absorb microwave energy, so only the last class is of particular interest. Good absorbing

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material must combine moderate values of ε’ with high values of tan(δ) [9]. Yet our material should not be to conductive – electrical conductor reflects microwaves. Most promising minerals are those that belong to semiconductors. This is because of higher penetration depth than for reflective materials and greater loss factor than for transparent materials. From these reasons microwave heating devices, that usually are working on materials with high water content, operate at 2.45 GHz. This is the frequency at which the water is lossy enough to heat efficiently, but at the same time it is not to reflective. The maximum of loss factor for water is peaking at around 20 GHz. In the same manner we should think about pigments and paint ingredients. We have seen that some of pigments contain charcoal, carbon black and graphite [11], which might be excellent microwave absorbers. Dielectric loss tangent of charcoal varies between 0.11 – 0.29 at 2.45 GHz and at room temperature, so it is higher than tan(δ) of distilled water. Dielectric loss tangent of carbon black lies between 0.35 – 0.83 at the same frequency so it is quite high. It is important to say that pure graphite is not a good microwave absorber, because it is well known as good electrical conductor. On the other hand over the years graphite powder has been used in microwave absorbing materials, when mixed with rubber to lower its overall conductivity. We may say that graphite as crystal will reflect microwaves but graphite as powder with bound water should be good absorber. At the same time we should look at the loss factor of wall structure, very often they are made from brick, limestone, sand and concrete. Table 1. Relative permittivities and loss tangents for materials at around 2.45 GHz (and at 22OC if not otherwise specified) Material coal charcoal carbon black concrete (dry) concrete 5000PSI after 38 days mortar cement after 38 days green granite white marble green granite white marble calcite (CaCO3) 60OC dolomite (CaMg(CO3)2) 60OC pyrite (FeS2) 60OC

Freq 2.45 2.45 2.45 2.45 2.45 2.45 2.03 2.02 3.31 3.21 2.216 2.216 2.216

ε’ 4.5 6.25 4.4 7.75 8.63 7.76 8.61 2.89 2.89 7.07

tan(δ) 0.02-0.08 0.11-0.29 0.35-0.83 0.0111 0.048 0.045 0.0144 5.09 10 4 0.0193 5.99 10 4 0.0085 0.0161 0.1503

source [9] [9] [9] [12] [13] [13] [13] [13] [13] [13] [14] [14] [14]

1.2. Fresco preparation techniques In [15] some popular investigation methods applied to the works of art are studied. The method presented in this paper may by considered similar to the infrared reflectography. We have made an assumption that usually a wall consists of some kind of brick or conglomerate which is plastered with lime. The old fashioned plastering techniques were of our interest. The true fresco is a painting made on wet plaster. Artists use natural pigments dissolved in lime water. Pigments must be alkali-proof (resistant to caustic limewater) [5]. The fresco technique may be considered similar to aquarelle. However, in contrast to aquarelle, the pigments and lime plaster bind

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together and thus they become integrated. The technique described here is called Buon Fresco and it make use only of natural materials. Fresco plaster is made from calcium lime putty and an aggregate consisted of is washed river sand, marble meal and volcanic tuff. The proportions will wary but are usually one part of lime putty and two parts of aggregate. Very often there are three to five plaster layers. In general the hidden layers contain more sand, and the sand is coarser there. Drying of lime plaster includes many physical and chemical processes such as absorption of water into wall, evaporation of water from the surface and carbonation of slaked lime by carbon dioxide: Ca(OH) 2 + CO 2 → CaCO 3 + H 2 O

(6)

According to many sources, a number of artists prepared full scale drawings of frescoes. The purpose of these drawings was a study of composition. There were important issues such as lights and shadows and other details of future frescoes. It is important to understand that it takes a lot of time to paint large fresco and that lime plaster is drying during work. So artists divide their work by decomposing one fresco into a set of sections called giornatas. Each section is small enough to be easily made in one day. Giornatas were sometimes marked or sketched using charcoal and this fact may be used for fresco unrevealing.

2. The experimental setup and results The experimental setup consists of a microwave heating device, thermovision camera (Flir E300, able to record hi-resolution - 240 x 340 - JPEG images) and test sample. The 1kW magnetron, powered by computer controlled switching power supply, was used as a microwave source. With the help of adjustable shorting back plate, the magnetron is coupled with rectangular waveguide. The distance between its open end and the tested sample may be manually changed, providing far-field working conditions. Due to safety purposes the experiment's taken place in antiecho chamber. The examined fresco model was placed directly below the open-ended waveguide and heated for 10 minutes with 1000 W of microwave power.

Figure 1. Experimental setup.

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Figure 2. Block diagram.

The graphite painting done on concrete block was used as an examined fresco model. Two straight lines painted using graphite containing pigment were modeling the fresco paining. This simple sketch was placed directly on the surface of the wall model. To simulate the concealment of the fresco, the painting was covered with dried gypsum plaster made on plywood - this

Figure 3. Examined fresco model (w/o and with plaster cover).

First, the microwave heating rates of charcoal, marble brick and plaster piece were compared. Examined materials were heated for 5 minutes using 1kW of microwave power.

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Figure 4. The microwave heating rates of charcoal, marble brick and plaster piece. From left to right: Before heating in visible light , before heating in IR and just after heating in IR

Thermogams below present temperature distribution on the surface of fresco before and just after microwave heating. Next, thermal images of wall model were acquired during cooling phase. Simple image processing algorithms were used to reveal fresco sketch from obtained thermograms

Figure 5. Thermograms w/o plaster cover. From left to right: Before heating, just after heating and after 10 min of cooling

The set of pictures above presents the uncovered fresco; The one below – shows fresco covered with plaster.

Figure 6. Thermograms with plaster cover. From left to right: Before heating, just after heating and after 10 min of cooling

Fresco model with and without plaster cover was heated for 10 minutes. The difference between the thermogram taken immediately after heating, and the thermogram taken after 10 minutes of cooling, shows the inner structure of the wall fragment as well as the fresco contour.

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Figure 7. The difference between the thermogram taken immediately after heating, and the thermogram taken after 10 minutes of cooling. Left: w/o plaster cover, right: with cover

3. Conclusions The method described here may be used not only for revealing fresco, but also for imaging of the inner structure of the wall. Additional study, including advanced image processing techniques, should be carried out in order to more accurately fresco shape recognition. The method could be used for crack detection (upper right corners of concrete block in Figure 7), because the heat from inner heat sources propagate through air filled cracks very slowly. References [1] On-site investigation techniques for the structural evaluation of historic masonry buildings BAM, SLG and partners (IaFB, IDK), November 2004 [2] N.P.Avdelidis, M.Koui, C. Ibarra Castanedo, X. Maldauge, Thermographic studies of plastered mosaics, Infrared Physics & Technology, 49, (2007), 254 256 [3] N.P.Avdelidis, A.Moropoulou, Applications of infrared thermography for the investigation of historic structures, Journal of Cultural Heritage, 5 (2004) 119 127 [4] Robert Osiander, Jane W.M. Spicer, Time resolved infrared radiometry with step heating a review, Rev. Gén. Therm., 1998, 37, 680 692. [5] Tessa Lindsey, Fresco Painting: The Dichotomy of Rigorous Craft and Artistic Expression, NLA International Building Lime Symposium 2005, Orlando Florida, 2005, Building Lime Group. [6] E. T. Thostenson, T. W. Chou: "Microwave processing: fundamentals and applications", Composites: Part A 30 (1999) 1055 1071. [7] Metaxas A. C., Meredith R. J.: Industrial microwave heating, Peter Pereginus Ltd., 1983. [8] M. C. Corbeil: "Application of X ray diffraction in conservation science and archeometry", International Centre for Diffraction Data 2004, Advances in X ray Analysis, Volume 47 [9] J. A. Menendez, et. al.: "Microwave heating processes involving carbon materials", Fuel Processing Technology 91 (2010) 1 8 [10] Hua Yixin Liu Chunpeng, Heating Rate of mineral and Compounds In Microwave Field, Transactions of NFsoc Vol.6 No.1, 1996 [11] D. Hradil, J. Hradilová, S. Švarcová, E. Kotulanová, Hand Held XRF for the Preliminary Screening of Early Romanesque Frescoes in Slovakia, 9th International Conference on NDT of Art, Jerusalem Israel, 25 30 May 2008 [12] Rohde & Schwarz Application Note, Measurement of dielectric material properties, 2006 [13] J. Baker Jarvis, M.D. Janezic, B.F. Riddle, R. T. Johnk, P Kabos, C.L. Holloway R. G. Geyer, C. A. Grosvenor, Measuring the Permittivity and Permeability of Lossy Materials: Solids Liquids Metals, Building Materials and Negative – Index Materials, Technical Note 1536, The National Institute of Standards and Technology, 2005 [14] S. Marland, A. Merchant, N. Rowson, „Dielectric Properties of Coal”, Fuel (80), 2001, 1839 1849 [15] W. S. Taft, J. W.Mayer, „The Science of Paintings”, Springer Verlag, New York, 2000

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Solid Materials Complex Permittivity and Inhomogenities Determination in High Frequency Range Dagmar FAKTOROVÁ Department of Measurement and Applied Electrical Engineering, Faculty of Electrical Engineering, University of Žilina, Slovak Republic

Abstract. The paper is devoted to dielectrics from more standpoints. A practical method for dielectric constant determination with fully unknown dielectric properties is given. Particular attention is paid to the influence of dielectric fillings in the crack in metals and the processes of defects detection in dielectrics and metals are compared. The ability of microwaves to detect a conductive object under the dielectric surface has been demonstrated by a practical example. Keywords. complex permittivity, crack, NDT, microwave frequency, waveguide reflection method

Introduction The paper responds to technological practice needs, when the knowledge of complex permittivity is required, e.g. at manufacturing building slabs which are to safeguard buildings or their critical parts against microwave signal penetration [1], when the accurate estimation of crack dimensions in metal and dielectric sample in the case when the investigated crack is filled with dielectrics with unknown dielectric parameters is needed and when the crack presence and its dimensions assessment in dielectric sample is need to be estimated.

1. Complex permittivity dielectric sample with admixtures Since the building materials are mostly of dielectric character, it is possible to influence this required property by suitable admixtures. In spite of the fact that the dielectric properties of suitable admixtures are well known, their inclusion with the suspension material can result in dielectric with unexpected properties. The measurement of complex permittivity is the subject of many technical and scientific areas and an unambiguous determination of its value often runs into difficulties. Particularly in technical applications it is possible to notice a situation when e.g. two specimens of nominally the same material may have significantly different complex permittivity as a consequence of different manufacturing processes, different degree of oxidation and different inclusions. From the microwaves absorption’s point of view [2] the mean quantity is the loss factor, which is connected with the real part of complex permittivity. The problem

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comes down to the determination of relative permittivity of the building material with the suitable admixture providing the required absorption of microwave signal. For this purpose we use for dielectric constant İ measurement the waveguide reflection method, by which for the wavelength in waveguide Ȝgd filled with investigated dielectric holds [2]

λgd =

λ0 λ ε− 0 λc

,

(1)

where Ȝ0 is the wavelength in free space, Ȝc is the critical wavelength in the waveguide. By a simple arrangement of Eq. (1) for İ calculation we get

§ 1 1 · + . ¨ λ 2 λ 2 ¸¸ c ¹ © gd

ε = λ02 ¨

(2)

As Ȝ0 is known from the used frequency and Ȝc depends on the waveguide dimensions, it remains to measure the wavelength of electromagnetic wave in investigated dielectric materials Ȝgd. If it is a case of İ measurement (for loss tangent tgį determination it can be used an another method, e.g. resonant method), Ȝgd (respectively Ȝgd/2) can be measured on the measuring line by simple monitoring of the standing wave ratio (SWR) minimum on the slotted line by successive shortening of the sample. Equation (2) gives unambiguous determination of İ and if the suitable technique is available for the sample length changing, such unambiguous determination of İ is very effective and reliable. For individual lengths of the sample SWR is measured and results can be used for tgį determination, too. The known tgį value can be used for calculation of isolation panel with carbon admixture thickness in the case of electromagnetic shielding needs. In Fig. 1 there is plotted the dependence of SWR on the length of the sample manufactured from a chipboard containing 10% of carbon. From the measured values the wavelength in the sample for frequency 8200 MHz was found out: Ȝgd = 16.4mm (Ȝ0 = 36.6mm, Ȝc = 45mm). SWR [-]

f = 9,97 GHz 0,6 0,5 0,4 0,3 0,2 0,1 0 0

10

20

30

40

50

sample length [mm]

Figure 1. Dependence of SWR on the sample length for dielectric sample with carbon admixture (10%)

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2. Influence of dielectric in defect volume on the detected signal

Attention was paid to defects on metal surfaces to be detected by means of microwaves as reported by some researchers and particular results from this research can be found also in [3] with the appropriate theoretical analysis, where also further literary sources are given. In this section the attention is turn to the investigation of the microwave signal response in the case when dielectric filling occurs in the volume of the artificial crack introduced in the metal sample. When the waveguide track is terminated with the load, it can be characterised by complex loading impedance [1]

1 + ρ Z = Z 0 , 1 − ρ

(3)

where Z0 is the characteristic waveguide line impedance and ρ is the complex reflection coefficient. As all quantities on the right – hand side of Eq. (3) are measurable, the complex loading impedance of waveguide can be calculated. The measurements of complex impedance of waveguide load, represented in our case by the defect in metal sample filled with various kinds of dielectrics, were performed on the standard microwave track. The microwave track was equipped with the measuring line for SWR measurement and terminated with the open waveguide as a probe. This technique of an open-ended waveguide probe requires an accurate measurement of the complex impedance of waveguide probe opening which is in precise relation with the dielectric properties of crack filling and crack dimensions (Fig. 2). As a source of microwave signal HP signal generator was used.

Figure 2. Experimental set up for inhomogenities and dielectric parameters measurement, K – reflex klystron, KPS –klystron power supply, IM- impedance match, VA – variable attenuator, MT – magic T, A – adapter, FM – frequency meter, FI – ferrite isolator, CL – coaxial line, FM – frequency meter, WRS – waveguide rotation change–over switch, SWD – standing wave ratio measurement line, FC – ferrite circulator, CD – crystal detector, OW – open waveguide, SA – selective amplifier, MSH – movable sample holder

For the measurement an artificial rectangular crack (1mm wide and 8mm depth) in metal plate was fabricated. The measurements were performed for the crack with

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different dielectric fillings, (Table1) and the distance of the probe from the crack was 1mm. Table 1. The crack fillings dielectric properties İ of filling 1.0 2.1 3.0 4.5

crack filling air teflon plexiglas pertinax

tgį of filling 0 0.00028 0.00670 0.04600

The results for values of amplitude and phase of complex impedance for crack with dielectric filling in metal sample are in Fig. 3. From the results it can be concluded, that the dielectric filling of the crack in metal sample strongly influence the signal reflected from the inhomogenity represented by crack filled with dielectric. The absolute value and the phase of complex impedance of defect with dielectric filling investigated by the waveguide probe can assume an inductive and capacitive character. In case when the dielectric parameters of crack filling are known we can estimate the depth of defect with appropriate corrections of received reflected microwave signal. If we do not know the dielectric properties of the crack filling it is possible in case of inversion problems to solve for dimensions and the shape of crack to deliberate the presence of dielectric in the crack volume.

f = 9,97 GHz

1600

Im{Z}

Z|ȍ|

f = 9,97 GHz 1400

1200

700

800

0

-700

400

-1400

0 0

1

2

3

4

İ [-]

5

a)

0

350

700

1050

1400 Re{Z}

b)

Figure 3. Dependence of complex impedance a) amplitude and b) phase of crack with dielectric fillings with known dielectric properties

3. Investigation of defects in dielectric materials

The practical needs are often connected with requirements of defect in dielectric sample presence and with defect geometry knowledge. For this purpose in some cases it is sufficient to measure the inhomogenity response on the microwave signal passing over the investigated dielectric material. The pertinax plate (İ = 4.1, tgį = 0.046) specimen with dimensions: the width 150mm, the length 150mm and the thickness

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20mm with introduced artificial notch with dimensions the width 0.2mm, length 10mm and the depth 3mm was used in experiments. The measurements were performed on the measuring waveguide line terminated with an open waveguide used as a probe. The probe was moved over the defect filled with air and SWR was measured. Dependence of complex impedance amplitude and phase of the investigated defect on probe position is shown in Fig. 4. f = 9,97 GHz Im{Z}

|Z| [ȍ]

f = 9,97 GHz 100 80

80

40

60

0

40 -40

20 -80

0 -10

-5

0

5

-80

10

-40

0

40

80 Re{Z}

probe position [mm]

a)

b)

Figure 4. Dependence of complex permittivity a) amplitude on probe position and b) Lissajouse curve

To investigate the influence of lift off on the reflected crack signal in the pertinax plate sample the amplitude of the reflected microwave signal from the dielectric sample was measured. The measurements were performed at two positions of the pertinax sample with artificial defect – close to the sample and at the distance of 5mm from the waveguide probe from the side of open effect (OD) and the side of closed defect (ID). The recorded results are given in Fig. 5. f = 9,97 GHz, liftoff - 0mm

f = 9,97 GHz, liftoff - 5mm

100 am plitude [a.u.]

amplitude [a.u.]

125

100

75

80

60

50

40 25

20 -15

0 -20

-10

0

10

probe position [mm] ID

a)

-10

-5

0

20

5

10

15

probe position [mm] ID

OD

OD

b)

Figure 5. Dependence of reflected signal amplitude on the probe position for ID and OD defect in pertinax sample , a) lift off 5mm, b) liftoff 0mm

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From Fig. 5 it can be seen, if the probe comes near to the defect from open side, the reflected signal amplitude changes promptly and in the case approaching from the lose side, the change in the reflected signal amplitude is slow (the distance of the probe from the defect is bigger and is equal to the depth of the dielectric behind the defect). f = 9,97 GHz, OD

f = 9,97 GHz, ID 120 amplitude [a.u.]

amplitude [a.u.]

100 80 60

100 80 60

40 40

20 20

0 -20

-10

0

0

10 20 probe position [mm]

0 mm

-15

-10

-5

0

5 10 15 probe position [mm]

5 mm 0 mm

a)

5 mm

b)

Figure 6. Dependence of reflected signal amplitude on the probe position in pertinax sample for two distances of the probe from the sample with defect

Surprisingly, the values of the reflected signal from the close and open side of defect can be seen at first sight. But considering the fact that at measuring for different sample distances from the probe also the phase effect applies, this fact is acceptable. As an illustration we performed also measurements demonstrating this fact and the dependences of the reflected wave amplitude on the sample distance from the probe are shown in Fig. 6. Should the need arise to measure defects from different distances (lift off) we have made complete this effect of phase influence on the course of reflected signal with continuous changing of the probe distance from the defect and the results are in Fig. 7 for pertinax sample from open side and close side of the defect. f = 9,97 GHz

amplitude [a.u.]

100 80 60 40 20 0 0

1

2

3

4

5

6

7

liftoff [cm] ID

OD

Figure 7. Dependence of reflected signal amplitude on the distance of the probe from OD and ID defect in pertinax sample

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4. Conclusion

Experimental results mentioned in the individual chapters confirm the ability of microwaves to detect the defects in dielectric materials. For the better outlook at practical measurement and considering material properties theoretically, measurement for reliable determination of fundamental dielectric materials determination where performed. For the practical evaluation of the signal reflected from the defect, the signal shapes at the probe moved horizontally over the defect and at moving away from the defect were investigated by the open waveguide method. It is possible from our measurements in microwave frequency range to perform the following evaluations: the presented results showed that the method is suitable for medium – loss materials dielectric properties measurement because at high – loss materials the determination of wavelength in investigated dielectric material is difficult. Our measurement method proves the possibility unambiguous value of İ assessment. The method can provide the reliable information about the microwave attenuation in various admixtures composed from dielectric materials with different dielectric properties. Our experimental results showed influence of crack dielectric filling on the reflected microwave signal from the defect in metal sample. The open waveguide method is suitable for nondestructive testing of dielectric samples with introduced crack. Our results showed the ability of crack characteristics investigation from open and closed side in microwave frequency range.

Acknowledgements

The author would like to thank MSc. Pavol Žirko director of High School for Agriculture and Fishing in Mošovce for technical help at realization of experiments. The author would like to thank to Prof. Ivan Makovíny for providing the samples for this work. The work has been done in the framework of Slovak Grant Agency APVV Project No. SK-RO-0015-10.

References [1] M. Pastorino et al.: A global optimization technique for microwave. nondestructive evaluation, IEEE, Transaction on Instrumentation and Measurement 51 (2002), 666-673. [2] D. Faktorová: Some experiences with microwave investigation of material defects, Studies in Applied Electromagnetics and Mechanics 31 (2008), 162-170. [3] D. Faktorová: Utilisation of microwaves material defect investigation. Acta Technica CSAV, 53, (2008), 17-27. [4] D. Faktorová, K. Grondžák: Microwave Measurement of Biological and Allied Materials, Proceedings of the APMC 2006 conference, Yokohama, Japan, (2003), 544-547. [5] B.M. Maškovcev, K.N. Cibizov, B.F. Emelin: Teorija Volnovodov, Moskva-Leningrad, Nauka, 1966.

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Terahertz Time Domain Inspection of Composite Coatings for Corrosion Protection a

Przemyslaw LOPATOa,1, Tomasz CHADY a and Joao M.A. REBELLO b Department of Electrical and Computer Engineering, West Pomeranian University of Technology, al. Piastow 17, 70-310 Szczecin, Poland b Laboratory of Nondestructive Testing, Corrosion and Welding, Department of Metallurgical and Materials Engineering, Federal University of Rio of Janeiro, CEP 21941-596, Brazil

Abstract. Terahertz radiation is sensitive to refractive index variations and is strongly reflected by conducting objects, thus it is an effective tool in nondestructive evaluation of protective coatings of steel. In this work a composite material consisting of a paint layer, polymeric layer, ceramic layer and a steel plate in its interior was examined. Typical applications are: storage tanks for petroleum, diesel, aviation fuel, diesel, crude oil, salt water, gasoline, alcohol, process and transport of chemical products, platforms and offshore structures, electrolytic cells, anodizing lines, stations water and wastewater treatment, water tanks in the chemical, petrochemical and chlorine alkali plants. Evaluated test specimen contains manufacturing flaws in the metal/ceramic layer interface. Because of multilayered structure of the coatings, time domain measurements with very short THz pulse duration (~20 ps) were utilized in presented experiments. Defects were detected by reflection imaging based on pulsed terahertz TDS (Time Domain Spectroscopy). Selected THz B scans in case of non defected and defected area are shown. Dedicated defects detection algorithm is proposed and verified. Results achieved during terahertz inspection are compared with those obtained using active thermography. Keywords. THz imaging, time domain inspection, corrosion protection, defects detection algorithms

Introduction Terahertz imaging become more and more popular NDT technique. Usage of high frequency electromagnetic waves restricts its applicability to dielectric and semiconductor materials volumetric examination. Only surface of conducting materials can be inspected, but for this case several other and cost-effective techniques exists, like eddy current testing ECT, magnetic flux leakage MFL or visual inspection.

1

Corresponding Author: Przemyslaw LOPATO, Department of Electrical and Computer Engineering, Faculty of Electrical Engineering, West Pomeranian University of Technology, al. Piastów 17, 70 310 Szczecin, Poland, E mail: [email protected]

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Terahertz inspection seems to be very good choice for examination of metallic parts composite coatings. Opposite to ultrasonic technique (also applicable in coatings inspection) the use of coupling medium is not necessary. Due to large differences in absorption coefficient of coating (ceramics and polymers) and core material (steel plate) and a relatively small loss of material occurring in the case of delamination, radiography is not sufficient method of such structures inspection. The paper shortly introduces to specific type of coating applied in industry (e.g. oil or chemical industry). Also some basic information about terahertz technique are given. Then the results of THz time domain inspection of composite anticorrosion coating are presented. Next dedicated defects detection algorithm is proposed and verified by results of active thermographic imaging.

1. Anticorrosion coatings Many construction materials suffer from corrosion, which causes degradation of their lifetime. For this reason such structures are often covered with an anticorrosion coating. In order to assure sufficient strength, the coating must be mechanically and thermally suited to the base material, mostly steel. This condition is fulfilled only if coating fabrication process does not produce defects. An example of composite coating is presented in Fig. 1. The sample consist of an anterior coating with esther-vinyl epoxy novolac resin strengthened with glass fibres. The coating was applied in three layers composed of primer, mortar reinforced with glass fibre plated with impregnation resin, veil of surface also impregnated and finishing with resin. The base metal was blasted mild steel with a profile of 70 m. The total dry thickness of the coating is approximately 6 mm. Typical applications of such coatings are: storage tanks for petroleum, diesel, aviation fuel, diesel, crude oil, salt water, gasoline, alcohol, process and transport of chemical products, platforms and offshore structures, electrolytic cells, anodizing lines, stations water and wastewater treatment, water tanks in the chemical, petrochemical and chlorine-alkali plants.

Figure 1. View of anticorrosion coating sample.

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2. Terahertz reflection imaging Terahertz electromagnetic radiation (T-ray) enables non-invasive, non-ionizing and non-contact examination of dielectric materials such as: plastics, dry wood, ceramics, foams and composites [1]. The T-rays are sensitive for refractive index, thus any defect which disturbs it, e.g.: • void, • delamination, • inclusion, • material inhomogeneities (fiber/matrix distribution), • surface roughness, • fiber waviness, • internal interfaces between layers (in layered structures) can be detected. In most cases, defects are located by reflection pulsed terahertz TDS (Time Domain Spectroscopy) [2]. The method is well suited for evaluation of layered materials. Each interface between separate layers causes reflection of incident THz pulse and attenuation of transmitted one. Differences in delays of the propagated pulses and their echo (delayed layer reflections) enable characterization of the thicknesses and inner structure state. Very short pulses (order of picoseconds) contain wide frequency bandwidth (0.05 - 3 THz) and therefore it is possible to carry one single point broadband measurements.

2.1. Imaging system Simplified scheme of terahertz time domain imaging system is shown in Fig. 2. The main components of the system are: • pair of transducers (transmitter and receiver), • ultra fast laser, • optical delay line. THz pulses are generated and picked up by photoconductive antennas (PCA) [3]. The main part of the THz transmitter is bowtie antenna with photoconductive gap, which is illuminated by femtosecond laser pulses. Such excitation and application of external DC bias causes pulsed current flow through metallic part of antenna. The currents induce electromagnetic wave. The resulting bowtie antenna radiation is collimated by high resistivity hemispherical silicon lens and then focused on examined object surface by High-Density PolyEthylene (HDPE) lens. View of measuring heads in reflection arrangement is shown in Fig. 3. During our measurements we applied TRay4000 imaging system of Picometrix, which offers the frequency resolution of 3 GHz and average power of THz beam – less than 500 μW. Lateral resolution of TDS technique is less than 200 μm and depth resolution less than 50 μm [4].

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Figure 2. Simplified scheme of the measuring system.

Figure 3. View of the measuring system.

2.2. Results of measurements B-scan signal obtained by reflection inspection of delaminated composite anticorrosion coating using terahertz technique is shown in Fig. 4. In case of nondefected area one can observe two pulses caused by: • front surface reflection, • steel plate reflection. Any additional pulse is caused by a defect. Position of such pulse (related to surface and plate reflection pulses) carry an information about defects depth. In case of defected area such additional pulse arises in vicinity of base material reflection pulse, thus the detected defect is a delamination (air gap) between steel plate and ceramics.

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Using THz time domain technique we are able to measure also the thickness of the coating based on time delay ΔtD between both pulses, however this parameter is not a good one in order to detect delaminations (information about the coating thickness is insufficient). In examined sample there were delaminated areas having smaller thickness than other locations without defects.

Figure 4. Measured B scans in case of non defected (left) and defected (right) area.

3. Defects detection 3.1. Algorithm Block scheme of proposed defects detection algorithm is presented in Fig. 5. THz inspection needs a raster scanning in x-y directions. In each (x,y) position an A-scan signal (as shown in Fig. 6) is acquired. One can see there are two main pulses (front surface and steel plate reflection). For each of them some features were calculated, e.g. MaxVal – maximum value of the pulse and its position (time delay tD) – MaxPos. After extraction of waveform features, their two dimensional maps are created (e.g. MaxPos (x,y)). Achieved maps contain an information about the coating thickness and possible defects. The thickness information is strongly correlated with low frequency component of the 2D feature map. This trend may be calculated and eliminated from 2D signal, leaving only information about defects. The most important step is trend calculation. It is based on background elimination procedure applied before in digital X-ray imaging [5]. Background (or trend) is obtained using median filter with relatively big mask size . The best results were achieved in case of 60x60 points square window of median filter. An elimination of trend was obtained by its subtraction from the original map. Then the signal was thresholded and the result indicates defects positions.

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Figure 5. Block scheme of defects detection algorithm.

Figure 6. Measured A scan with indication of separate reflections and several waveform features.

3.2. Results of defects detection The results achieved for both sides of examined composite coating specimen are shown in Fig. 7 and 8. Both figures show detrended two dimensional distributions of selected waveform feature (MaxPos(x,y)) and final signal after thresholding operation. Results achieved using time domain THz technique were validated using active thermographic inspection. Thermal excitation of the specimen was done using inductive heating of base material (steel plate). This kind of thermal excitation causes a temperature growth from interior part of the specimen. Thermal image was acquired using thermographic camera, during heating process. One can observe similarities of the results in case of both techniques.

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Figure 7. Results of THz inspection specimen side without visible defects in crossection (upper part in Fig. 1).

Figure 8. Results of THz inspection specimen side with visible defects in crossection (lower part in Fig. 1)

Figure 9. Results of thermographic inspection after 3s of inductive heating.(left: the same side as in Fig. 7, right: as in Fig. 8)

4. Conclusions In this work pulsed time domain terahertz imaging of composite anticorrosion coatings was presented. Complex coating with manufacturing defects was examined. Dedicated defect detection algorithm was proposed and validated using results of THz measurements and thermographic inspection. Obtained results enable to form a conclusion that pulsed THz inspection with proposed defects detection algorithm are effective tool in nondestructive testing of composite anticorrosion coatings of metallic base materials.

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Acknowledgments This work was supported in part by the State Committee for Scientific Research, Poland under Grant (N N510 538039) “Badania nieniszcz­ce materiałów kompozytowych falami elektromagnetycznymi w pa®mie cz¯stotliwo®ci terahercowych”/ “Nondestructive testing of composite materials using terahertz frequency electromagnetic waves” (2010-2012).

References [1] [2] [3]

[4]

[5]

D. Zimdars, G. Fichter, A. Chemovski, Time domain terahertz computed axial tomography for nondestructive evaluation, Review of Quantitative Nondestructive Evaluation, vol. 28 (2009), 426 433. D. M. Mittelman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, M. Koch, Recent advances in terahertz imaging, Applied Physics, Lasers and Optics, B 68 (1999), 1085 1094. I. S. Gregory, C. Baker, W. R. Trib e, I.V. Brad ley, M.J. Evans, E.H. Lin field, A. G . D a v i e s , M . M i s s o u s , Optimization of Photomixers and Antennas for Continous Wave Terahertz Emission, IEEE Journal of Quantum Electronics, 41 (2005). 717 728. D. Zimda rs, J. A. Va ldmanis, J.S. White, G. Stuk, S. Willi amson, W.P. Win free, E . I. M a d a r a s , Technology and applications of terahertz imaging non destructive examination: Inspection of space shuttle sprayed on foam insulation, Review of Quantitative Nondestructive Evaluation, vol. 24 (2005), 570 577. R. Sikora, P. Baniukiewicz, T. Chady, W. Rucinski, K. Swiadek, M. Caryk, P. Lopato, Comparison of selected weld defects extraction methods, , Review of Quantitative Nondestructive Evaluation, vol. 27 (2008), 1034 1041.

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SIMULATION ASSISTED DIAGNOSTIC OF SWITCHING ARCS Hans-Peter SCHMIDT a,1, Michael ANHEUSER b, Sylvio KOSSE c University of Applied Sciences Amberg-Weiden, Amberg, Germany b Siemens AG, Amberg, cSiemens AG, Erlangen, Germany

a

Abstract. A diagnostic method for low voltage switching arcs is proposed where the magnetic field of the switching current is used to determine the arc movement. The magnetic field of the switching current density is recorded with an array of field sensors. The time and space resolved readings are compared with results from simulations of the arc. Parameters of the simulation and therefore current densities are adapted to reconstruct the measurement readings. So an inversion of the ill conditioned integral equation is not necessary. Results with a hardly optimized set up showed that this approach may be successfully applied to measure arc movements. Keywords. Switch gear, arc simulation, measurement of arc movement, Hall sensor array

Introduction Applying arc modelling to circuit breaker design implies a trade off between detailed physical modelling and necessary simplifications. While simplifications might neglect even dependencies relevant for results an accurate detailing is still not feasible [1]. Only adequate measuring techniques may verify the actual model for the required purpose. Low voltage circuit breakers exhibit an arc in air within a complex shaped arc chamber. Usually the arc is quenched, when the voltage drop exceeds the voltage of the grid. This voltage drop is achieved by driving the arc into stacked splitter plates. The dielectric recovery of the residual gas mixture determines the re-ignition behaviour. The breaking behaviour of medium circuit breakers depends also heavily on arc movement and high voltage switch gear is also strongly dependent on arc movement. The actual arc movement is crucial for the overall quenching process. Figure 1 gives a cross sectional view of two different types of low voltage circuit breaker which are equipped with stacked splitter plates.

1. Arc modelling An overview of relevant arc models is given by Anheuser [1]. The governing equations of magneto-hydro-dynamics for a single fluid consist of the energy conservation 1

Hans Peter Schmidt, h.schmidt@haw aw.de, Kaiser Wilhelm Ring 23, 92224 Amberg, Germany.

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equation (1), the momentum (2) and mass conservation (3) extended by species conservation (4).

Figure 1 Cross sectional view of miniature circuit breaker (left) and a circuit breaker (right). Figures are not to scale.

Because we deal with fast flowing gas, the energy equation is formulated in total enthalpy, to account for kinetic energies h=hstat+1/2 u2. Enthalpy changes are balanced by heat conduction, radiative cooling/heating and Joule heating.

& & ∂ (ρ h ) + ∇ $ (ρ h u& ) = ∇ $ (Γh ∇h ) + E $ j − s ∂t

(1)

h enthalpy, ρ density, u velocity, heat conduction: Γh λ/cp diffusion coefficient, cp specific heat, E j Joule heating; s radiation losses

In low voltage circuit breakers, shock waves influence the characteristics of an arc considerably. To model this type of gas flow the momentum conservation becomes the transient compressible Navier-Stokes equation, where the Lorentz forces constitute the source term. As the operating gas is Newtonian the stress tensor with the dynamic viscosity ° may be used [1]. If we denote density W, thermal conductivity ¬, velocities u, time t and pressure p, the transient compressible Navier-Stokes reads [1][2][3]:

& & & ( & & &&& ∂u ρ + ρ u ∇ u = −∇ p + ∇ $ τ + j × B ∂t

(

)

(2)

p pressure , τ friction stress tensor , u velocity, j x B Lorenz force

Equation (1) and (2) are completed by the mass conservation (3) and may be extended by species conservation (4) if ablation is to be considered [1].

& ∂ρ & + ∇ $ (ρ u ) = 0 ∂t

(3)

H.-P. Schmidt et al. / Simulation Assisted Diagnostic of Switching Arcs

& & & ∂ (ρ Yi ) & + ∇ $ (ρ Yi u ) = ∇ $ Γi ∇Yi ∂t

(

)

427

(4)

Yi Species , Γi diffusion coefficient for species Yi

The current density is calculated from a generalized Ohms law taking movement into account (5). The magnetic field is derived from a standard vector potential formulation (6).

& & & & j = −σ ∇Φ + σ u × B

& § & 1 *· & ∇ × ¨¨ ∇ × A ¸¸ = j μ ¹ ©

(5)

(6)

Field diffusion within the magnetic splitter plates is neglected. This set of equation may be even more extended by equations for arc root movement or general arc wall interaction, respectively. Likewise radiation may be formulated with net emission coefficients or may be detailed by solving a simplified radiation transfer equation [1] [2] [3]. Material properties such as thermal and electrical conductivity are derived from minimizing Gibbs function with a Chapman-Enskog procedure. The material properties are then functions of temperature, pressure and concentration. These coupled equations may be solved with finite volume codes [1] or with coupled FEM and FVM procedures. Existing 2-D and 3-D codes are applied to calculate the temperatures and therefore current densities. Figure 2 gives results from such calculations. A snap shot of a typical temperature distribution is given for different models of the arc root movement. FVM is applied for solving the fluid dynamics part. This is realized by the commercial CFD solver CFX 11 with additional user defined functions. Maxwell’s equations are solved with the finite element method applying edge based elements of low order. For this task ANSYS 11 is used as the electromagnetic solver. The meshes consisted of approximately 300000 cells for the finite volume mesh with a similar spatial resolution for the FEM code. The data is mapped onto the meshes by interpolation using a next neighbour search.

Figure 2 Calculated temperature distribution for a miniature circuit breaker as given in figure 1 [4]. Different models for arc roots were used for the two results. Temperature ranges from an ambient value of 300K to approximately 20000K.

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H.-P. Schmidt et al. / Simulation Assisted Diagnostic of Switching Arcs

2. Arc diagnostics Integral quantities such as voltage and total arcing currents may be recorded. Likewise pressures at specific positions may be taken directly from measurement readings. Temperatures are usually assessed by spectroscopic means and tomographic procedures yield the distributions. This diagnostic method suffers from the following uncertainties: Radiation may be totally or partially reabsorbed and the cold gas at the fringes blurs images and actual gas composition e.g. metal vapour concentrations influence the readings [5]. For accessing the arc movement one resorts to high speed cameras, where the intensity which enters the camera lens is recorded. Here the relative brightness is taken for the current density distribution. Commonly intensity readings are taken from a single line of sight and no tomographic procedures are applied. Still the above mentioned difficulties are present [6]. As a simulation assisted approach the intensities at the outer edge of the arc are computed from the solution of equations (1) to (6) and compared with camera readings [6].

3. Magnetic Diagnostics of Arc Movement To determine the time dependent current density distributions the following procedure is assessed. The magnetic field outside the circuit breaker is recorded via a Hall sensor array. Readings are then compared to calculated field strengths. While previous work assumed that current paths are a succession of rectilinear and threadlike segments [7] we propose to use either the self consistent (1) to (6) solution or a 3-D FEM solution of (6). The self consistent solution of equations (1) to (6) has to be used only if all details are of interest. Clearly, current densities themselves are more efficiently deduced from equation (6) only. Therefore we solve (6) for a variety of sets of reasonably guessed current distributions taking into account that saturation of the splitter plates sets in at high current values. The current distributions are then adjusted to yield the measured magnetic field strengths. These calculations are carried out with the Vector Fields 3D Opera suite. Figure 3 gives an example of calculated magnetic inductions for an assumed current path and the according breaker geometry.

Figure 3 Calculated magnetic induction for a given current path. The simulated breaker is shown on the right.

H.-P. Schmidt et al. / Simulation Assisted Diagnostic of Switching Arcs

429

4. Measurement of the Magnetic Field To demonstrate the feasibility, we use a scanning magnetic camera. A circuit breaker with a fixed current path is scanned with magnetic field sensors. The measuring device consists of an L-shaped Hall–sensor array. This array consists of two times 8 sensors with perpendicular orientation. A 3-D precision positioning device provides a scanning volume of app. 0,3 m x 0,3 m x 0,4 m with a spatial resolution better than 0,2 mm. Readings are provided by a multi-channel electronics for the Hall probes, an analogdigital conversion with 1 MHz bandwith and a computer control. Figure 4 gives a schematic view of the experimental set-up for the circuit breaker with a fixed current path.

5. Results Instead of an actual arc a fixed current path within the breaker was used. With the scanning device we recorded field patterns as depicted in figure 5. Readings of the Bx component shown were taken at a fixed z-position corresponding to the breaker housing. The spatial resolution was 1 mm covering an area of 80 mm x 80 mm. This region is also shown in the left part of figure 4.

Figure 4 Schematic and actual view of the measurement setup

We record the Bx and By components of the field at each point. But for clarity we considered here only the Bx component of the field. One recognizes the straight part of the current path close to the lower half of the region at the position x= 20 mm. The dilution of the field at a height of y=30 mm to approximately 50 mm corresponds to the position of the steel splitter plates. The U-shaped current feed in the upper half gives the varying field levels of the Bx component. To demonstrate the general feasibility of our approach we solved equation 6 utilizing the Vector Fields Opera 3D software. We used the known breaker geometry and guessed a reasonable current path. As the essential a priori information we use the approximate distance of the current path from the sensors plane. Still this guessed current path differed from the one we have set out for our measurement considerably.

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We adjusted the x- and y-position of a current segment according to difference in the measured and calculated field maximum. Figure 5 gives the result for such a single iteration.

Figure 5 Measured (left) and calculated (right) magnetic induction; Bx component. Field levels range from 0 20mT.

As expected, we found reasonable good agreement between the given current path and the one obtained from the calculation for straight paths, despite using one iteration only. We have been able to reconstruct the U-shaped section of the current path approximately using only the Bx and By component. For the region with the splitter plates we found it difficult to adjust the current path according to measurement. The restricted dynamic range of our measurement did not provide sufficient detailed readings. We found the measurement of the two field components Bx and By sufficient to approximately reconstruct the current path, which we reduced to a path in one plane. For further investigations we will need to measure all three components of the magnetic induction. For the relatively small currents of 100-200A, which we used here, the region with steel splitter plates could not be resolved. Nevertheless applying real breaking currents of some kA will yield magnetically saturated plates and therefore magnetic field levels which will be used to determine the current path. We expect that the suggested procedure may be successfully applied to determine a real arc movement if a magnetic camera with an appropriate bandwidth is used instead of our scanning device.

References [1] M. Anheuser, C. Lüders, Numerical Arc Simulations for Low Voltage Circuit breakers, Proceedings XVIIIth Symposium on Physics of Switching Arcs, 2009 Brno, Czech Republic [2] U. H. Bauder, H. P. Schmidt, Arcs, Sparks and Other Discharges, Encyclopaedia of Applied Physics, Editor L. Trigg, VCH Publishers NY, 1995 [3] H. P. Schmidt, G. Speckhofer, Experimental and Theoretical Investigation of High Pressure Arcs Part I and II, IEEE Trans. On Plasma Science (34) (1996) 1229 1238 and 1239 1248 [4] Hauser et al., Proceedings 19. Albert Keil Kontaktseminar, 2007 Karlsruhe, Germany [5] H. P. Schmidt, M. Anheuser, S. Kosse, Arc Modelling in Low Voltage Switch Gear, Proceedings GEM XVI, 2010 ,Murramarang, Australia

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[6] S. Kosse, C. Lüders, C. Hauser, Switching Arcs: Comparability of Simulations and Experiment, Proceedings XVIIIth Symposium on Physics of Switching Arcs, 2009 Brno, Czech Republic [7] C Brdys, et. al., Optical and Magnetic Diagnostics of the Electric Arc Dynamics in a Low Voltage Circuit Breaker, Meas. Sci. Technol. 13 (2002) 1146 1153

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Studies on Analysis Technique of Commutation Phenomena for Cleaner’s Universal Motor Using the State Variable Method a

Yuji AKIYAMAa,1 and Yuta NIWA a Kanagawa Institute of Technology, Japan

Abstract. This paper focuses on the restraint method of the 3rd harmonics current, which close attention has been paid to the iron core shape of the universal motor for power vacuum cleaners. In this paper, the air gap permeance, magnetic saturation of an iron core, and the influence a slot ripple has on the harmonic current were verified using FEM electromagnetism analysis. As the result, stator core shape proved quantitatively that a restraint of harmonic current has effect. The authors assert that a design manual should be adapted to create international standard about a restraint of the harmonic current of a universal motor. Keywords. universal motor, commutation phenomenon, finite element method, state function

Introduction Today, many electronic appliances are driven by an inverter to achieve high efficiency. As a result, under the influence of a capacitor input type commutation circuit, a big current distortion arose for the electric power system, the serious problems, such as a transformer and a phase advance capacitor can be occurred big damage. The regulation of harmonic current restraint represents an international problem. In this paper, we explore the restraint technique of the harmonic current of universal motors. The harmonic restraint technique described in this paper didn’t use neither a reactor nor an active filter. We did study the harmonic restraint paid the iron core shape for a universal motor. This verifies quantitatively air gap permeance ripples, iron core saturation, and the influence of a slot and pole shape ripples. The result proved quantitatively that a harmonic restraint has an effect according to expansion of an air gap size on the pole edge, and the conditions of stator magnetic pole shape and the iron core characteristics of the material. Therefore, the authors assert the iron core design manual of the universal motor about a harmonic restraint which carries out international standard conformity was able to be shown. In addition, the targeted model machines are input power 1.5kw and a 33,000rpm high-speed universal motor for cleaners.

1

Corresponding Author. Kanagawa Institute of Technology, 1030 Shimo ogino Atsugi shi Kanagawa ken, Japan; E mail: office@sml nb.co.jp; Tel: +81 462 91 3233

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1. Application of Power Supply Harmonic Current Restraint Standard 1.1. IEC Standard (international standard) and a JIS Standard (in Japan) The targeted testing machine is targeting the vacuum cleaner of input voltage AC200V and 1.5kW of input electric power in this paper. As for the international standard about the harmonic current restraint applicable to this apparatus, IEC61000-3-2 and "the limited value over the apparatus (below the input 16A) connected to a general lowvoltage power distribution system" correspond. However, the limit value under the supply-voltage 220V is not prescribed by IEC61000-3-2. In Japan, two or more guidelines related with a harmonic current restraint were published. For examples, JIS-C-61000-3-2 "Electromagnetic compatibility (EMC)-Part 3-2: Limits for harmonic current emissions (equipment input current ู20A per phase)" was enacted in 2003. This aims at consistency with an international standard in Japan where the electric input power base differs from that European one. 1.2. Application of IEC Standards First, application of the harmonic restraint standard in this paper is defined. In this paper, since the target universal motor assumes the use of a vacuum cleaner, it applies the vacuum cleaner of IEC61000-3-2. A vacuum cleaner is classified into a classification "Class A" of apparatus. The harmonic current limit of Class A is shown in Table 1 here. In this paper, it is satisfied with a motor only, the substance of these harmonic current limit values, and aims the design manual which suppresses reduction performance for the minimum. In addition, by the standard, which apparatus with the regulating function of power consumption is described controlling phase angle as 90±5 degrees such severe. However, in this time, our target is sine wave drive only, this means no use of harmonics filter. 1.3. Calculation of Harmonic Currents The measurement apparatus of the harmonic current is specified to IEC61000-3-2. In this paper, the distortion of the waveform of the current was measured by the high speed digital oscilloscope, and Fourier transformation of [Discrete Fourier Transform (DFT) was used it] (1).

ck =

1 N −1 2π · § ki ¸ ⋅ ¦ xi ⋅ exp¨ − j N i =0 N ¹ ©

, k = 0,, N − 1

(1)

2. Simulation of the Harmonic Current using FEM Electromagnetic Field Analysis 2.1. Outline of an Target Machine The sectional view of the iron core of the universal motor used for this analysis is shown in Fig. 1. This design dimensions and rating are shown in Table 1. The Slot’s combinations are 22slot/2pole, and the total numbers of commutator segments are 22

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Y. Akiyama and Y. Niwa / Studies on Analysis Technique of Commutation Phenomena

bars. Moreover, the armature winding is lap winding. (Refer to Fig.2). Moreover, the spatial relationship of Raiser and winding has placed the brush at the neutral point, when a magnetic field system is the weakest including armature reaction. Table 1 reveals that this motor is considerably more high-powered than a Japanese standard cleaner motor (inputs 900W and 100V) for home use. The motor used in this experiment is a high-output cleaner of 200V system, commonly used in Europe and the U.S. These are equivalent to a business-use cleaner in a Japanese market. In Japan, is no connection terminal wire to the 200V power source; however, it is a standard system type in Europe and North America. Table 1. Motor’s specification Input Voltage

200 V / 50 Hz

Input Max Power

1,500 W

Rotational Frequency / Min.

33,000 r/min

Field Winding

˳0.5 106Turn / Pole

Armature Winding

˳0.4 30Turn / Slot

Air Gap

0.5 mm

Core Thickness

21.0 mm

Iron Core Material

Silicon Steel Plate (50A1300)

Figure 1. Cross section of universal motor’s core.

Figure 2. Figure of armature winding & brushes and poles arrangement.

2.2. Harmonic Current Analysis by Non linearity of Iron Saturation In order to conduct to the harmonic current analysis, there is the necessity of computing input current distortion correctly. The measured waveform of the input voltage at the time of the sine wave drive, in the radical model described above to Fig. 3(a) and current was shown. An analyzed simulation result was shown in Fig. 3(b). Comparison of both will obtain very good coincidence. This frequency analyzed result is shown in Fig. 4. The result is checked, that it was less than 5% of error although perfect coincidence is not said.

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Y. Akiyama and Y. Niwa / Studies on Analysis Technique of Commutation Phenomena

    







  

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(a) Measured results (b) Simulated results Figure 3. Voltage and current waveform (control angle 0 deg.).

Figure 4. Frequency analysis result of harmonics current

3. The Restraint Technique of Harmonic Current 3.1. Air-gap Size The analyzed figure model is shown in Fig. 5(a). This is a common technique used in Europe to suppress a steep current distortion by taking a large gap on the pole edge size, and satisfies an IEC standard. However, generating torque becomes problematic. Harmonic current is shown in Fig. 5(b), and when the air gap size was 1.0mm or more, the result of EMC’s standard could be satisfied. D  PP E  PP F  PP

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(a) Shape of analysis model (b) Analysis result of harmonic currents Figure 5. Change the harmonic current at the time of changing the length of an air gap.

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Y. Akiyama and Y. Niwa / Studies on Analysis Technique of Commutation Phenomena

3.2. Non Uniformed Air Gap Length Concept of State Function Calculation The calculation model was changed, the stator pole side shape of air gap length in Fig. 6(a), that compared it. The analyzed result of harmonics current was shown in Fig. 6(b), and that difference was insubstantial. The harmonic current resulting from a slot ripple reflects is very high frequency. Therefore, it does not influence in the order of low frequency waves. Our hypothezis is that the harmonics of a lower degree will not be greatly affected. Moreover, in the separate torque analysis conducted by our team, the mitigation effect of the torque ripple which aligned with Rota Tooth’s cycle was accepted. From this result, the constant length of air gap (a) type of a stator pole, can not be expected cause reduction of a torque ripple. Dಬ QRQ XQLIRUP D

DLUJDS PPᨺ PP XQLIRUP DLUJDS  PP

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(a) Pole shape of analysis model (b) Analysis result of harmonic current Figure 6. Change the harmonic current at the time of changing the length of unequal Air gap shape.

3.3. Stator Pole tip’s face Geometry The analysis model figure which made thickness of the stator pole the parameter is shown in Fig. 7(a). This figure considers the influence on the harmonics of the magnetic saturation phenomenon at the tip of a stator pole portion. A large pole angle is seen here, as well as the magnetic saturation at the pole tips, suggesting a reduction of the harmonic current. However, since the magnetic saturation phenomenon at the stator chip indicates an improvement of a commutation phenomenon has much effected, further research are required and need it. G  PP H  PP I  PP

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(a) Shape of analysis model (b) Analysis result of harmonic current Figure 7. Change the harmonic current at the time of changing the stator pole tip’s thickness.

Y. Akiyama and Y. Niwa / Studies on Analysis Technique of Commutation Phenomena

437

3.4. Influence by the Iron Core Material The influence on the harmonic current at the time of changing by the iron core material into 50A1300 from the silicon steel plate 50A800 was also considered in our research. In addition, the analysis models that are the gap shape and length such as 0.5mm of air gap, and 1.5mm of stator chips. By the harmonic current that result in this analysis is shown in Fig. 8. It is more improvement are possible, by using the iron core material of high Bmax iron core, then raise a torque, than this result. As expected, this has an effect of a restraint of harmonics current. Our results shows that iron core material and quality has a drastic impact on harmonic current, and should be considered along with cost.

Figure 8. Change the harmonic current at the time of changing the core materials.

4. Conclusions In this paper, we consider the influence of the core shape and iron core material upon the harmonic current. The valuation basis was based on the IEC standard. The evaluation technique was examined using FEM electromagnetism analysis. This strict analysis utilized various functions, such as brush contact resistance, which changes with rotation, in this FEM electromagnetic was analyzed by FLUX-2D. We also took into account variated state functions, such as brush contact resistance, commutation phenomena and used iron core shapes, Air gap length, etc. As a result, the power supply current distortion waveform and simulated results has good mashing was able to obtain the waveform was very similar to an actual measurement result. In this paper, we can show the result quantitatively that a restraint of harmonic current has an effect under the influence real iron core shape and the characteristics of the materials. Although it corresponds by addition of a reactor, etc. conventionally in many cases, naturally there is a problem of increased cost. Therefore, current harmonics are controlled by the design of iron core shape. The balance of a restraint of operation characteristics and harmonic current should be maintained. By using the methods that mentioned above, we assert that iron core shape and performance (considering cost optimization) should be implemented into the design process.

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Y. Akiyama and Y. Niwa / Studies on Analysis Technique of Commutation Phenomena

References [1] Yuji Akiyama, Toshiyasu Takura, Yuta Niwa : “A study about Core shape Design of 200V Lines for Vacuum Cleaner Universal Motor”, The paper of Technical Meeting on Rotating Machinery, IEE Japan, No.RM03 137, pp.7 12 (2003) (in Japanese) [2] S.Suzuki, K.Kurihara, H.Nase, K.Takahashi : “RF Noise Associated with Time Varying Arc Current across Brush and Commutator in Universal Motors”, T.IEE Japan, Vol.118 D, No.6, pp.773 779 (1998) (in Japanese) [3] H.Koharagi, K.Tahara, Y.Ishii, S.Suzuki : “Application and Evaluation of Commutation Performance with an Exceptional Armature Winding Form for Small Universal Motors”, T.IEE Japan, Vol.115 D, No.4, pp.488 494 (1995) (in Japanese) [4] Yuta Niwa, Mithuhito Kawamura, Yuji Akiyama : “Request of technological points for vacuum cleaner motor in 200V system”, The paper of Technical Meeting on Rotating Machinery, IEE Japan, No.RM04 168, pp.45 50 (2004) (in Japanese) [5] R. Richter : Elektrische Maschinen ൙ (1950) [6] IEC 61000 3 2, Electromagnetic compatibility (EMC) Part 3 2: Limits for harmonic current emissions (equipment input currentู16A per phase)

Electromagnetic Nondestructive Evaluation (XIV) T. Chady et al. (Eds.) IOS Press, 2011 © 2011 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-60750-750-5-439

439

Propositions for the Analysis of Commutation Phenomena of Universal Motors Using the State Function Method a

Yuji AKIYAMAa,1 and Yuta NIWA a Kanagawa Institute of Technology, Japan

Abstract. The universal motors of our advanced research use FEM simulations to perform modeling of universal motors rotating at ultrahigh speed, by using the like state function method with respect to the details regarding the commutation scintillation or arc phenomenon of the commutators, the air gap surface, and its contact condition of the brushes. As a result, at the design stage, the commutation scintillation phenomenon was quantitatively estimated and an investigation was performed with respect to the configuration of the iron core. Furthermore, an example of this modeling method based on FEM analysis was performed with regard to the electromotive force of the transformer effect, the armature reaction and the scintillation voltage including the contact resistance of the brushes resulting from the rotation, the configuration of the iron core, and the changes in the gap permeance. Regarding the validity of this analysis, an extremely close match was attained between the results of the present simulation and the experimental results. In this regard, the targeted model motor was a 1.5 kW, 33,000rpm ultrahigh speed, high capacity universal motor for cleaners. Keywords. universal motor, commutation phenomenon, sparking voltage, finite element method(FEM), state function

1. Analysis Technique of Harmonic Current for Universal Motor 1.1. Outline of the Object Machine The sectional view of the iron core of the universal motor is shown in Fig. 1. The design dimensions and rating are shown in Table 1. The Slot combinations are 22slot/2pole, and the number of commutator segments is 22 bars. Moreover, the armature winding is lap winding. (Refer to Fig.2) Table 1 reveals that this motor is considerably more high-powered than a Japanese standard cleaner motor (inputs 900W and 100V) for home use. The motor used in this experiment is a high-output cleaner of 200V system, commonly used in Europe and the U.S. These are equivalent to a business-use cleaner on the Japanese market. In Japan, although there is no track record in 200V power supply; however, it is a standard system type in Europe and America.

1

Corresponding Author. Kanagawa Institute of Technology, 1030 Shimo ogino Atsugi shi Kanagawa ken, Japan; E mail: office@sml nb.co.jp; Tel: +81 462 91 3233

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Y. Akiyama and Y. Niwa / Propositions for the Analysis of Commutation Phenomena

Table 1. Motor’s specification Input Voltage

200 V / 50 Hz

Input Max Power

1,500 W

Rotational Frequency / Min.

33,000 r/min

Field Winding

˳0.5 106Turn / Pole

Armature Winding

˳0.4 30Turn / Slot

Air Gap

0.5 mm

Core Thickness

21.0 mm

Iron Core Material

Silicon Steel Plate (50A1300)

Figure 1. Cross section of universal motor’s core.

Figure 2. Armature winding & brushes and pole’s arrangement.

1.2. Analysis Method This analysis simulation became the coupling analysis of the iron core geometric model and external circuit which was taken in as a state variable. First, model is made with the finite element method in the state element shown in Fig. 4, and considering the spatial relationship of the space. Moreover, the external circuit shown in Fig. 3 is equivalent to the circuit composition of all universal motors[4]. The relations arrangement and number of rotations of an external circuit and an iron core geometric model have been preestablished. Furthermore, the voltage equation by electromagnetism circuit combination (which added the conditions of equation (1)) has been formed. The details are given below:

L

di RT ­RT ½ + iR+ ® b ¾(I + i) − b (I − i) + ec = 0 dt t ¯T − t ¿

(1)

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Y. Akiyama and Y. Niwa / Propositions for the Analysis of Commutation Phenomena

Here, it is R=Rc+R1 (Rc is coil resistance, Rl is resistance of the lead which conducts a coil to commutator bars.). T is the value which shaped brush width, and is divided by speed of the commutator or the commutation cycle, and t is time (second). ec represents the electromotive force "commutation electromotive force" by a commutation[1][5]. Equation (1) is the first order differential equation, and L, R, and T are circuit constants and time in this formula. Moreover, t and i are variable constants, although it is not a variable: here, the portions related to change of a state variable are the 3rd term and the 4th term. That is, the contact resistance Rb of a brush is expressed in the shape of a temporal response. In this analysis, it is considered as change of brush part resistance of the external circuit shown in Fig. 3 means contact of the brush and commutator’s contact resistance[4]. The contact surface product of a brush and a commutator bar carries out modeling as brush contact surface product change, which shows signs that it changes by the rotation angle ± in Fig. 5 (a). If this contact surface product is treated in the form of a differential equation as a temporal response by rotation angle degree ±=²t of an armature, it will change, as shown in Fig. 5 (b). In addition, contact resistance changes with the reciprocal of this contact surface product. L of equation (1) is the inductance of a commutation coil, and is computed in finiteelement-method, magnetic field analysis from the shape and material characteristics of an iron core, or the number of turns of winding. In addition, the normal magnetization curve is used for the nonlinear one of the iron core to simplify our analysis. Moreover, the induced voltage generated in a commutation coil becomes a relation of equation (2). Usually, there are two types divided, roughly into the speed electromotive force of the 1st terms, and the transformer electromotive force of the 2nd terms:

e = −L

di § dφ dθ di · =¨ ⋅ +M ¸ dt © dθ dt dt ¹

(2)

This first term changes with magnetic resistance that change of a air gap magnetic parmiance; harmonic current and commutation sparks are influenced by slot shape, shape of a stator magnetic pole, and air gap length. The problem of commutation sparks or EMC is later explored in this analysis. It is related with change of the leakage reactance of the coil that mainly related with the position of overlap condition of slots and magnetic poles. The simulation has been done for the all of the 22 pieces of coil in a slot was shown in Fig. 3 and Fig. 4, is carried out by small rotation at a angle (ຒ˥ = 1 deg.) within every cores and rotor stator angles. With the conventional method, slot opening and magnetic pole shape are taken in to the shape of the state variable of a air gap face by this method to dealing with magnetic flux density as fixed. And the simulation is carried out to revolving speed ², most important changing factors considered have been taken into account. And magnetic flux density in the air gaps, will calculated by remains magnetic flux, or induction voltages etc can be done by finite-element-method of electromagnetic field analysis. In addition, FLUX-2D of this laboratory and the Grenoble University (France) (CEDRAT) of the joint research point and Ver.7.6 are used for this analysis.

Y. Akiyama and Y. Niwa / Propositions for the Analysis of Commutation Phenomena

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Figure 3. External Circuit figure for universal motor simulation.

Figure 4. Figure of armature winding, brush, pole’s arrangement.

θ bru + θ bar G=

1 Roff (a) Contact condition of modeling figure.

θ bru − θ bar

1 Ron



− θ pos

− θ pos + 360

θ

(b) Modeling figure of contact area & resistance.

Figure 5. Figure of armature winding, brush, pole’s arrangement.

1.3. Analysis Conditions Physical quantity required for this analysis as well as models and the finite element method in expression of the state element are shown in Fig. 4, and is inputting iron core shape by CAD. Moreover, a normal magnetizing curve are used iron core maker’s published data. In the external circuit shown in Fig. 3, the source of voltage (voltage and frequency), a brush and it’s overlap condition (whole surface contact resistance, brush width, and commutator-bar width) of a commutator bar, armature winding (a number of turns and DC resistance), and magnetic field system winding (a number of turns and DC resistance) are listed. In addition, the ratio of brush width to commutator-bar width is set to 2.0 (brush covering ratio). Analyzed conditions are based on the rated operational status of the real machine shown in Table 1. A total of 3960 steps are analyzed between 20msec, 1 cycle of a 50Hz power supply will using as 1 step of 33,000rpm, rotations and a rotor rotates 1 degree of analysis step angles.

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443

2. Proposed New Testing Method The appearance of the voltage measuring device between commutator bars devised for the purpose of commutation waveform observation of an actual armature coil is shown in Fig. 6, and the model figure of the testing equipment is shown in Fig. 7. This is the new system device at our laboratory. This test equipment has 2 slip rings for observing the voltage and current of commutator-bars No.1 and No.2. Coil current is picked out from these two slip rings outside through the brush of an upper left part. That is a system which carries out direct measurement of the commutation short-circuit current waveform which flows into the object of armature coil. This equipment takes out a commutation waveform from the commutation coil of a real machine directly. Therefore, the measurement of the waveform in which all the state variable elements were included is possible. The state variable are slot shape, the overlap condition of a brush and a commutator bars, influence of iron core saturation, etc. In addition, this equipment can change a brush covering ratio and a brush shift position easily. This equipment can be used as a means by which more complicated and details of a future commutation phenomenon are verifiable. 3LFNXS %UXVK

&RPPXWDWRU 1R

1R 6OLS 5LQJ Figure 6. New measuring testing contrivance for commutation our proposed testing equipment figure of voltage and current.

Figure 7. Model figure of testing device for contact area of brush and commutator bars.

2.1. Analysis Conditions The measurement result is indicated to a typical principle figure of equivalent commutation phenomenon test equipment with Fig. 8. This result and the proposal method of us, if it compares, it will result in the following conclusions. ((1)-(5)) (1) Core shape is not taken into consideration. (2) The short-circuit current between commutators is immeasurable. (3) In our proposed method, the current value and potential difference of each commutator bar are correctly and direct measurable. (4) The naming of measurement system (Fig. 6 and 7) by the proposal of this Akiyama and Niwa’s method so calls Akiyama & Niwa’s method. (5) The spike noise between the commutators shown in Fig.10 (Brush commutation’s spike voltage is not including the polarity of AC power supply voltage)

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Y. Akiyama and Y. Niwa / Propositions for the Analysis of Commutation Phenomena

Figure 8. Figure of equivalent commutation phenomenon test equipment.

3. Analysis of Commutation Phenomenon 3.1. Comparison of the voltage wave analysis between commutator bars, and a measurement result A high-precision dynamic analysis of the commutation coil by brush and commutator’s, which is the energy source, will required of the analysis of a commutation sparking phenomenon. The analysis of the commutation voltage between two commutator bars is analyzed. For example, the result having compared, the analysis and the measurement of the voltage waveform of the coil (a) of Fig. 2 is shows in Fig. 9. It can be said that the analyzed value and the actual measured one are well in accord from the waveform of this figure (a) & (b). This measured result, indicates the voltage waveform obtained by our method, the electric potential measuring device between commutator bars shown in Fig. 6. Therefore, the influence of air gap’s magnetic permeance distribution is reflected. The analyzed value is based on analysis with the high accuracy described previously.

Figure 9. Voltage waveform of armature coil.

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445

The analysis waveform very similar to a measurement was obtained. This analysis method was able to take in the important variable factors as a state variable. The detailed elucidation of a commutation phenomenon and a commutation problem elucidation are possible with this method. In addition, under the present circumstances, commutation sparks and EMC are average value calculations, and neither a slot nor magnetic pole shape is taken into consideration[11]. 3.2. Examination of brush sparking voltage analysis In the universal motor for ultra high-speed kW class cleaners, the analysis of sparking voltage is an advanced technology and is an ultramodern technical development, because the analysis of sparking voltage is a key factor of the brush life of the present bottlenecked problem. This problem is a cutting-edge subject globally. Here, the analysis result of commutation sparking voltage is shown in Fig. 10. This is an example of sparking voltage analysis that compared with low resistance graphite brush and the high resistance carbon brush. In comparing these results, so, the latter of a spike voltage will high with a low resistance, brush (A) has occurred at the time of commutation. On the other hand, in the case of a high resistance brush (B), it has reduced sharply of sparking voltage. 

/RZ 5HVLVWDQFH %UXVK $



+LJK 5HVLVWDQFH %UXVK %

9R WDJH > 9@

     







5RWRU $QJOH > GHJ@







Figure 10. Calculated brush voltage waveform.

Also, these results are in accord with the sparks generating phenomenon of DC motor. The reason compared with the sparking voltage of DC motor, there are few reports of the sparking voltage of an alternating current drive universal motors. Therefore, it judged that it was better to compare with the sparking voltage waveform of DC motor. As compared with a measurement result, and our new proposed FEM simulated basic voltage waveform are very good congruous. However, the spike voltage of the latter is not much congruous. This reason have addition of the contact state of a brush and commutator’s, the influence of a factors, the temperature rise of a contact surface, and vibration of a mechanical system other than the influence of an analysis step angle. Therefore, the

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reproducibility of this analysis is not so good. Naturally, the waveform of an actual measurement is also always changed and is not constant. Also, there is the necessity of inquiring further from now on. However, we introduce the result of the our present level of Fig. 10.

4. Conclusions A complicated commutation phenomenon peculiar to a universal motor is treating many factors as a state variable, and high-precision analysis has been realized. The importance of analyzed these phenomena quantitatively is large. Therefore, we think that future EMC correspondence and a commutation sparks problem can be coped with. We think that these techniques will be helpful in the elucidation of the commutation sparks phenomenon.

References [1] R. Richter : ಯElektrische Maschinen ൙ರ, (1950) [2] Donald G. Schultz, James L. Melsa : “STATE FUNCTIONS AND LINEAR CONTROL SYSTEMS”, McGrwa Hill Book Company (1967) [3] Richard P. Feynman : ಯThe Feynman lectures on physicsൗರ, (1986) [4] (France) CEDRAT SA : “FLUX2D®, Users Guide Vol.3” [5] Y.Akiyama : “The comparison of the characteristics in INV drive BLDC motor and Brushed DC motor”, The paper of Technical Meeting on Rotating Machinery, IEE Japan, No.RM01 162, pp.19 23 (2001) (in Japanese) [6] Y.Akiyama, T.Takura, Y.Niwa* : “A study about Core shape Design of 200V Lines for Vacuum Cleaner Universal Motor”, The paper of Technical Meeting on Rotating Machinery, IEE Japan, No.RM03 137, pp.7 12 (2003) (in Japanese) [7] H.Koharagi, K.Tahara, Y.Ishii, S.Suzuki : “Application and Evaluation of Commutation Performance with an Exceptional Armature Winding Form for Small Universal Motors”, T.IEE Japan, Vol.115 D, No.4, pp.488 494 (1995) (in Japanese) [8] S.Suzuki, K.Kurihara, H.Nase, K.Takahashi : “RF Noise Associated with Time Varying Arc Current across Brush and Commutator in Universal Motors”, T.IEE Japan, Vol.118 D, No.6, pp.773 779 (1998) (in Japanese) [9] K.Kurihara, S.Sakamoto, : “Starting Preformance Analysis for Universal Motors by FEM”, IEEJ Trans. IA, Vol.126, No.2, pp.124 130 (2006) (in Japanese) [10] K.Tahara, T.Takura, : “Trend of High Performance Universal Motors”, The paper of Technical Meeting on Rotating Machinery, IEE Japan, No.RM98 32, pp.77 82 (1998) (in Japanese) [11] S.Wagatsuma, T.Ueno, N.Morita : “Considerations for commutation theory by residual current, using commutation testing machine ”, The paper of Technical Meeting on Rotating Machinery, IEE Japan, No.RM02 23, pp.7 12 (2003) (in Japanese) [12] Y.Niwa, T.Naruta, Y.Akiyama : “Consideration about the core shapes, generating Torque, and Commutation phenomena of an ultra high speed Universal motor”, ICEMS2006, DS3F2 01, (2006) (Nagasaki, Japan) [13] Y.Niwa, Y.Akiyama, K.Miyazawa : “Nonlinear FEM simulation of the Commutation Sparking phenomenon of an Ultra High Speed Universal Motors”, EPNC2008, pp.95 96 (2008) (Lille, France) [14] Toshio Fuji, “Study of the universal motor” (1977) (in Japanese) [15] IEC 61000-3-2 : ಯElectromagnetic compatibility (EMC) Part 3-2, Limits Limits for harmonic current emissions (equipment input current ู 16A per phase)ರThird edition (2005)amendment1 (2008) [16] JIS C 61000 3 2 : ಯElectromagnetic compatibility (EMC) Part 3 2, Limits emissions (equipment input current ู 20A per phase)ರ (2003) [17] JIS C 9108 : “Electric vacuum cleaners” (1992)

Limits for harmonic current

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Detection of CFRP’s degradation through electromagnetic procedures Bogdan SERGHIAC1, Daniel Petrica SALAVASTRU2, Paul Doru BARSANESCU2, Adriana SAVIN3, Rozina Steigmann3 and Raimond GRIMBERGa3 1 University Al.I.Cuza, Iasi, Romania 2 Technical University Gh.Asachi, Iasi, Romania 3 National Institute of Research and Development for Technical Physics, Iasi, Romania

Abstract. Carbon fiber reinforced plastics, due their average electrical conductivity of the reinforcement, can be nondestructively evaluated by electromagnetic procedures. In the case of reinforcement from carbon fibers woven, to improve the spatial resolution of the image of the conductivity, we propose the using of a circularly aperture, very small, placed at short distance from the surface to be controlled that can diffracts the evanescent waves. By this procedure, the image of the reinforcement woven is observed, the delamination due impact with low energy being clearly distinguished. Keywords. Carbon fiber reinforced plastics, electromagnetic nondestructive evaluation, image reconstruction

Introduction Carbon fiber reinforced plastics (CFRP) have now applications from most different starting with aerospace industry and finishing with sports goods. CFRP have evolved both in reinforcements and matrix. From the point of view of the reinforcement, the tendency is to pass from pre-preg laminas at which the carbon fiber are parallel arranged to laminas that contain woven of different types of carbon fibers, leading to the improvement of formability of these composites. The carbon fibers have an average electrical conductivity around 103y104S/m and relative magnetic permeability is 1 [1]. The epoxy resin was the most usually the matrix for CFRP. Due to the facts that its mechanical properties are influenced by the moisture content and at temperature exceeding thermal destruction temperature, the resin relieves dangerous vaporous, the tendency is to be replaced it by Polyphenylene sulphide (PPS). This plastic material is less influenced by the moisture content and the quantity of noxious vaporous at high temperature is low [2]. The matrix has low electrical conductivity <10S/m and is paramagnetic. The specific degradations of CFRP are [1] x delamination due to impacts, even at low energies, or overloading of the structures x debonding between different reinforcement layers and matrix a

Corresponding author: email [email protected]

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x excessive porosity x water adsorption In present, C-scan or top view ultrasound, Lamb waves using non-contact transducers [3], with Hertzian contact [4] or compression waves generated by normal transducers or phased array [5] are used for nondestructive evaluation of CFRP. Also, active thermography [6] is used with good results and for debonding evaluation bond tests can be used [7]. The fact that in CFRP, the carbon fibers of average conductivity are embedded into an electrical insulating matrix has suggested that electromagnetic evaluation methods can be also utilized. These can emphasize the structure of fibers in the case of uniaxial laminas [8] or delamination due to impacts that lead to plastic deformation of composite, accompanied by important modification of transversal conductivity [9]. The modeling of electromagnetic nondestructive evaluation starts from the idea that one lamina can be considered as an anisotropic electric conductive plan, having different conductivity along the direction of carbon fibers and perpendicularly on them [10]. The entire composite can be modeled as a succession of thus plane, in thickness, having the direction of anisotropy axis according to the composite layout. The calculation of eddy current induced in different lamina can be effectuated, for example, using the dyadic Green’s functions method and the integral on the source’s volume method 10]. This procedure can be used to solve the forward problem for CFRP with different cracks that affect the fiber layers. However, in reality, the carbon fibers are not disposed in composite in parallel; electrical contact might be among fibers that form a lamina and between different lamina, schematically presented in Figure 1.

Figure 1. Possibilities of carbon fibers disposition in CFRP

This situation modifies the electrical conductivity local and completely randomly both in the plane of the fibers and perpendicularly on fibers. Another possibility for electromagnetic nondestructive evaluation of CFRP consist in considering the CFRP slab as a lattice of conductive threads and “illumination” of the slab with a plane wave [11]. The scattered field can give information about fibers layout. It must be mentioned that this model has only principle value, the situation presented in Figure 1 limiting the application possibilities. This paper proposes the nondestructive electromagnetic evaluation of CFRP reinforced with carbon fibers woven fabric using an absolute send-receive transducer working at hundreds of MHz frequency. The layout of fibers in woven, respectively the uniformity of arrangement becomes visible using Fourier optics methods.

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1. The field scattered by a conductive wire illuminated by a electromagnetic plane wave Let be an electromagnetic plane wave that illuminates a conductive wire, having diameter 2a, under an incident angle D, situation presented in Figure 2.

Figure 2. An electromagnetic wave encounters a conductive wire of diameter 2a and length L at angle D

According to boundary condition on the conductive surface

E inc  E scat

0

(1)

An expression is required to relate the current induced on a wire by an incident electric field to the scattered field it is produced. For a wire along Z-axis with a radius a of length L, the relation is [12]

d 2 A z  k 2 A z 2 dz A z

(2)

L /2

³ I  zc G  z, zc dzc z

(3)

 L /2

G  z, zc

2S

³ 0

R

j 4SH 0Z Ez  z

e jkR dI ' R

I'  z  zc  §¨ 2a sin ·¸ 2¹ © 2

(4)

2

(5)

where A is the vector potential, H0 is dielectric permittivity of vacuum, Iz is the amplitude of current induced in wire, G is the Green’s function of free space, k is the wave number. The incident electric field along the conductor from a plane wave at angle D is

Ez

e jk cosD sin D

(6)

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B. Serghiac et al. / Detection of CFRP’s Degradation Through Electromagnetic Procedures

This plane wave will drive the current in a symmetrical manner

I  z

I  z ; A z

A z

The final form of the integral equation of the wire current is L /2

³ I  zc G  z, zc dzc z

C1 cos kz  j

 L /2

4SZH 0 jkz cosD e k 2 sin D

(7)

The eq.(7) is a Fredholm integral equation of the first kind and C1 is an unknown coefficient that must be determined using, for example, block-pulse functions methods [13]. The radiation pattern of this wire is obtained as

f D

L /2

³ I  zc e

jkz c cos D

z

dzc

(8)

 L /2

and

F

20log10  f

[dB]

(9)

We consider an electromagnetic wave with the wavelength in vacuum 1m and the conductive wire has 0.8mm diameter, the same order of magnitude as of the carbon fibers and 1m length. The radiation pattern, F, is presented in Figure 3.

Figure 3. Radiation pattern for a conductive wire with 2a 0.8mm, L 1, O 1m

The radiation pattern from Figure 3 indicates the presence of a lobe for D=900 as well as a multitude of secondary lobes, with smaller amplitudes. A simple measurement of the scattered field might deliver very less information to made evaluation over some lattice of conductive fibers different oriented, as in the case of CFRP with reinforcement of carbon fibers woven.

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A possibility to enrich the quantity of information delivered by the electromagnetic examination of CFRP shall consist in the using of the evanescent waves diffraction, the waves that attenuate rapidly and can exist only in the immediate proximity of the material to be examined. The theoretical results presented in Figure 3 show thatthe optimal value for the angle D is S/2.

2. Studied samples Plates of CFRP made by TenCate-Netherlands, having 1.91mm and respective 4.2mm thickness have been taken into study. The plates have 6 and respective 12 layers of bidirectional 5Harness Satin fabrics (0,90,45) S as reinforcement, the matrix being from Polyphenylene sulphide (PPS). The examined plates are presented in Figure 4a. In Figure 4b is schematically presented the layout of the fibers in the carbon fibers woven, 5H satin type.

a

b

Figure 4. a) The examined CFRP plates; b) the layout of fibers in 5H satin.

The volume ratio of carbon fibers, warranted by the producer is 0.5r0.02. Some of the plates were impacted using a spherical bump-head, 22.5mm diameter, the impact energy varying from 0.5 to 4J.

3. Measurement equipment For electromagnetic evaluation of the studied composites, an absolute send receive transducer was used. The emission coil has 2 turns with 11.2 mm diameter, made from CuEm wire, 1mm diameter. The reception coil has also 2 turns, the average diameter being 3mm. The reception coil is placed coaxially with the emission one. The transducer is coupled with Network/Spectrum/Impedance Analyzer 4395A – Agilent USA. The transducer is mounted on a fixed support, the plate being displaced on two orthogonal directions with a displacing system, Newmark USA. The 4395A equipment is coupled with a PC through IEEE 488.2 interface. The displacing system is commanded by PC through RS 232 interface. The program for the command and acquisition is written in Matlab 2009a. In Figure 5a and b is presented the measurement equipment and respective, the transducer.

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B. Serghiac et al. / Detection of CFRP’s Degradation Through Electromagnetic Procedures

The lift-off has been maintained constant at 0.2mm. A region of 20x20mm has been scanned, the scanning step on both direction being 0.2mm. The examination had place at 100MHz, 200MHz, 300MHz and respective 400MHz, the real and imaginary component of the signal induced in the reception coil of the transducer being measured. After that, the same zones have been scanned with the same transducer but, a shield made from cooper sheet, connected to ground, has been placed in front of the reception coil, obstructing it completely. The shield has a circularly aperture of 0.25mm diameter.

a

b

Figure 5. The experimental set up: a) the equipment; b) the electromagnetic transducer

4. Results In Figure 6a is presented the dependency by position of the real component of the signal induced in the reception coil of the transducer at the scanning of a region of 20x20mm from a CFRP plate with 4.2mm thickness. The examination frequency was 400MHz. Although the lift-off was maintained at 0.2mm, the structure of the carbon fibers woven is almost non visible. To obtain a superior resolution, in front of the reception coil has been placed the circularly aperture. At the scanning of the same region, the image delivered by the assembly transducer-equipment is amplified. This is due to the diffraction on the aperture of the evanescent waves generated by scattering on the carbon fibers woven. The result is presented in Figure 6b. Considering an object placed in the plane z=0 and described by the function f0(x,y), at passing through an aperture, in the case of Fresnel diffraction (the aperture is closely to the object), the image obtained at the distance z from the object will be fz(x,y) and can be calculated using the algorithm presented in Figure 7, according to the principle of Fourier optics [14]. To ensure that fz(x,y) might represent exactly the figure of Fresnel diffraction through the a radius aperture, between the Fourier variables and the spatial ones must exist the relation

du

2a Ndx0

(10)

dv

2a Mdy0

(11)

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453

where N and M represent the maximum number of measurement points along x and y direction and dx0 and dy0 are the scanning step along x and respective y directions.

a

b Figure 6. The dependency by position of the real component of emf induced in the reception coil at the scanning of a 20x20mm region; lift off 0.2mm, frequency 400MHz: a) without aperture; b) with circularly aperture

The examination of data from Figure 6b shows that the structure of carbon fibers woven is clearly visible. f 0  x, y o

2 D Fourier Transform

F(0) (u, v) FZ (u, v) Inverse 2 D ª j 2S 2 2 2 º o x exp «   u v  » o Fourier Transform o f Z  x, y k ¬ ¼

Figure 7. The image through an aperture due Fresnel diffraction

Inverting the operation from Figure 7, the object f 0(x,y) can be determined knowing the diffraction figure fz(x,y). The measurements effectuated with the aperture

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make that the signals recorded shall represents f z(x,y). Applying the procedure described above, the shape of the object that scatters the electromagnetic field created by the emission coil can be determined. In Figure 8 is presented the image of the object starting from the Fresnel diffraction figure through a circularly aperture. Using this procedure, a region of composite with delamination due impacts has been examined. In Figure 9 is presented the region impacted with 2.5J energy on a CFRP plate with 4.2mm thickness.

Figure 8. The image of the object reconstructed from the image of Fresnel diffraction through a circularly aperture

Figure 9. The region impacted with 2.5J.

The analysis of the data from Figure 9 shows that the shape of delamination is visible. From the mechanics of composite materials [14] is known that, due to an impact normally on the surface of the composite, delaminations can appear, of whom

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455

shapes are approximately conical, fact visible in figure 9. By this procedure, the area of the delaminated surface can be determined; the method could become effective at the examination of CFRP. C-scan ultrasound using phased array allows the visualization only of delaminations due impacts with minimum energy of 6J, meanwhile our proposed method has an efficiency superior to the classical ones.

5. Conclusions Modern CFRP use more and more carbon fibers woven as reinforcement, instead of parallel fibers layers. For evaluation of these composites, a electromagnetic method based on absolute send receive transducer with the reception coil gathering the evanescent waves diffracted by a circularly aperture has been developed. In this way, the possibility to evaluate the state of the woven and the damages due to impacts with different energies can be substantially improved.

6. Acknowledgements This paper is partially supported by the Romanian Ministry of Education, Research, Youth and Sports under National Plan II - project MODIS 71-016/2007, Bilateral Project ENDE Ro-Si, and Nucleus Contract No.09430104.

References [1]. [2]. [3]. [4]. [5].

[6].

[7]. [8]. [9]. [10]. [11]. [12]. [13]. [14].

P.Morgan, Carbon fibers and their composites, Taylor &Francis, NY, 2005 http://www.tencate.com Z.Su, L. Ye_, Y.Lu,Guided Lamb waves for identification of damage in composite structures: A review, Journal of Sound and Vibration 295 754 (2006) 753 780 R.Grimberg, A.Savin, R.Steigmann, A. Bruma, P.Barsanescu, Ultrasound and eddy current data fusion for evaluation of carbon epoxy composite delaminations, INSIGHT, vol. 51, iss.1, (2009), pp.25 32. R.Grimberg, A. Savin, R.Steigmann, A.Bruma, P Barsanescu, D.Salavastru, , Determination of CFRP’s mechanical properties using ultrasound methods, Proceedings of NDT in Progress 2009, the 5th International Workshop of NDT Experts, Oct 12 14 2009, Prague, pp. 65 74 Y.Y. Hung, Y.S. Chen, S.P. Ng, L. Liu, Y.H. Huang, B.L. Luk, R.W.L. Ip, C.M.L. Wu, P.S. Chung , Review and comparison of shearography and active thermography for nondestructive evaluation, Materials Science and Engineering: R: Reports, Volume 64, Issues 5 6, (2009), pp. 73 112 W. Xue, L. Zeng, Y. Tan, Experimental studies on bond behavior of high strength CFRP plates, Composites Part B: Engineering, Volume 39, Issue 4, (2008), pp. 592 603 R.Grimberg, A.Savin, C.R.Rotundu, Eddy current microscopy applied to graphite epoxy composite, SENSORS AND ACTUATORS A PHYSICAL, 91, 2 1,( 2001), pp.73 75 R.Grimberg, D.Premel, A.Savin, Y.Le Bihan, D.Placko, Eddy current holography evaluation of delamination in carbon epoxy composites, INSIGHT, 43, 4, ( 2001), pp.260 264 H.A.Sabbagh, L.D.Sabbagh, Inversion of eddy current data and the reconstruction of flaws using multifrequencies, International Advances in Nondestructive Testing, vol 10, (1984), pp.307 332 J. D. Jackson, Classical Electrodynamics, Wiley: New York, 1998 R. Bancroft, Understanding Electromagnetic Scattering using the Moment Method: A Practical Approach Artech House, 1996 C.A.Balanis, Advanced Engineering Electromagnetics, John Wiley and Sons, 1989 J.W. Goodman, Introduction to Fourier, 2nd ed., Mc Graw Hill, NY, 1996

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Microwave Antenna Sensors for Fatigue Crack Monitoring Under Lap-joints Justin ERDMANN and Haiying HUANG1 Dept. of Mechanical and Aerospace Engineering, University of Texas Arlington, USA

Abstract. This paper presents a microwave antenna sensor that has the ability to monitor fatigue crack growth between lap joints where compressive force is present or in any other areas where a crack is hidden between two parts of a structure. The sensor is designed to be low profile, light weight, and conformal, making it ideal for aerospace applications and thus minimizing manual inspection times. The design of a fatigue sample to simulate a lap joint is presented. The antenna sensor was fabricated on the fatigue sample and tested under cyclic loading. The experiment results indicated that the microwave antenna sensor can monitor the crack growth as well as the crack orientation. Keywords. Antenna sensor, fatigue crack monitoring, structural health monitoring, Lap-joint

Introduction The integrity of engineering structures is one of the most important subjects to consider when designing and operating structures. In 1988, an Aloha Airlines Boeing 737 suffered substantial damage when an 18 foot section of the fuselage broke apart during the flight. After investigations, it was discovered that fatigue damage at a lap joint was the cause of the failure [1]. This accident highlights the importance of understanding and monitoring fatigue cracking in engineering structures. During designing, the engineers have limited information on the environment and the loading conditions that a structure will be exposed to. Despite the best engineering efforts, variations in structural loading or material decomposition due to corrosion cannot be fully accounted for during the design phase. As a result, fatigue cracking still remains an important safety concern. In addition, in many industries, such as aerospace, structures are being pushed beyond their intended design life and are expected to operate safely without losing their structural integrity. Even if the structure’s environment was predicted accurately, or even conservatively, pushing structures beyond their intended life will most certainly produce fatigue cracks. In order to ensure the continued safe operation of these structures, the cracks must be monitored, inspected, and repaired periodically. Visual inspection is the simplest method to monitor a structure but has many limitations, in addition to being tedious and time-consuming. For example, cracks may present in areas that cannot be easily viewed and may require the structure to be dismantled. In the aerospace industry, multiple days may be required to dismantle an aircraft, inspect it, and reassemble it, costing valuable time and money. Some lap joint 1

Corresponding Author ([email protected]).

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457

cracks may not even allow for visual inspection because disassembling these structures is usually impractical. In addition, visual inspection of these areas does not allow for continuous monitoring while the structure is in operation. Structural Health Monitoring (SHM) provides many options for inspecting and monitoring fatigue cracks under lap joints beyond the visual inspection method. One method for lap joint inspection is by piezoelectric ultrasound actuators/sensors [2]. By analyzing the reflected or transmitted propagating lamb waves within the material, cracks can be detected. However, the interpretation of the measured signals requires extensive signal processing [3, 4]. Acoustic Emission (AE) sensors can be used to detect fatigue crack growth while a structure is still in service [5]. The sensors operate by detecting the acoustic emission signals generated by a crack as it grows. Problems with this method are that the sensors are susceptible to outside noise sources and are unable to quantify crack size. The use of multi-frequency Eddy Current Imaging (ECI) is another method used to identify and monitor cracks in lap joints. An eddy current inducer was used to excite the structure to be inspected with an in-plane magnetic field [6]. A crack induces variations of the magnetic field distribution, which are linearly translated into variations of intensity of a light beam that can be measured by a CCD camera. The use of ECI requires a complicated set-up, and the presence of rivets may mask the presence of a crack, requiring extensive image processing. Recently, developments have been made in using Meandering Winding Magnometer (MWM) eddy current arrays for crack detection in lap joints [7]. As a crack propagates past the sensor, a change in conductivity is measured. In order to quantify the crack size, multiple channels must be monitored. Each channel requires a separate cable for signal transmission, adding unnecessary weight to an aircraft. The antenna sensor presented in this paper can be placed in between a lap joint and can withstand the associated compressive force. This enables the sensor to not only directly detect a crack, but also provide quantitative information on the size and direction of the crack.

1. Principle of Operation The antenna sensor that can monitor cracks under a lap joint is a slight modification of Ground Plane

Substrate

Width

Length

Metallic Patch

Crack in Ground Plane

Figure 1. Basic antenna sensor configuration.

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J. Erdmann and H. Huang / Microwave Antenna Sensors for Fatigue Crack Monitoring

Return Loss (dB)

0 -2 -4 -6

f01

-8 -10

f10 5

6

7 8 Frequency (GHz)

9

Figure 2. S11 curve of antenna sensor showing two resonant frequencies.

a regular antenna sensor, which is essentially a microstrip antenna [8]. A regular microstrip antenna, shown in Figure 1, has a simple configuration that consists of three main components: a metallic patch, a conductive ground plane, and a dielectric substrate. Together the patch and the ground plane form an electromagnetic (EM) resonant cavity. When used as a crack sensor, the structure acts as the ground plane of the antenna sensor. A feed line can be used to supply a radio frequency (RF) signal that excites the EM cavity at a particular resonant mode. The antenna sensor exhibits two fundamental modes of resonance, making up the S11 parameters shown in Figure 2. The f01 frequency corresponds to the radiation mode TM01, whose current flows along the length direction of the antenna patch; while the f10 frequency corresponds to the TM10 radiation mode whose current flows in the width direction of the antenna patch [8]. Each of the frequencies will be quantified by the return loss, with units of dB. As seen in Figure 2, both resonant frequencies are identified as the frequencies at which the return loss has a large dip. The resonant frequency of a regular patch antenna can be predicted using the transmission line model [9]. Based on this model, the frequency can be calculated by

fr 

c

1 . L  2 - re e 2%L

(1)

where c is the speed of light, re is the effective dielectric constant, Le is the electric length, and L the line extension. re can be calculated from the substrate thickness h, the dielectric constant of the substrate r and the antenna’s electric width we by the following equation

- re

- r 1 2



-r 1

2 1  10h / we 

.

(2)

The line extension value is calculated by %L  0.412h

- re  0.3 we / h  0.264 .

- re 0.258 we / h  0.813

(3)

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J. Erdmann and H. Huang / Microwave Antenna Sensors for Fatigue Crack Monitoring

By inspection of Equation 1, we can see that the resonant frequency of the antenna is inversely proportional to the electric length of the antenna patch, which is defined as the length of the current path along the current flow direction. For a perfect antenna patch and ground plane, the f01 frequency will be dependent on the geometric length of the patch and the f10 frequency will be dependent on the geometric width of the patch [8]. If a crack is introduced perpendicular to the electric length, however, the current flowing in the corresponding electric length direction will be forced to flow around the crack and the electric length will increase which reduces the resonant frequency. In addition to the extension of the current path, the antenna frequency will also respond to crack opening, which stretches the antenna patch and changes its dimensions. Therefore, both the effect of current length extension and crack opening will contribute to the decrease in the corresponding antenna resonant frequency. To monitor cracks under lap joints, the sensors need to be placed between two metallic pieces. A second substrate, i.e. the superstrate, can be introduced to electrically insulate the antenna patch from the top piece, creating a shielded microstrip antenna. The effect of the superstrate and the top ground plane on a regular microstrip antenna does not change the characteristics of the S11 curves enough to affect its performance, as evidenced by our results presented below. It is expected that crack presence in either of the ground plane will shift the corresponding antenna sensor frequency to a lower value.

Brackets

L Antenna Sensor

W

Crack Fatigue Sample

(a)

0.10

6.00 1.00

0.2

4.00 1.00

1.625

.375

3.25

1.00

3/8 2.00

(b)

(c)

Figure 3. Single lap-joint fatigue sample design; (a) exploded view. (b) fatigue sample. (c) holding bracket.

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J. Erdmann and H. Huang / Microwave Antenna Sensors for Fatigue Crack Monitoring

2. Fatigue Sample Preparation

In order to simulate a lap joint for fatigue testing, a test fixture consisting of a sample with a cracked hole and two brackets was designed and built. An exploded view of the single lap-joint test fixture is shown in Figure 3(a). The components were fabricated out of 7075-T6 aluminum with dimensions shown in Figure 3(b) and 3(c). Through-holes for 3/8 inch bolts were drilled at both ends of the sample and at one end of the holding brackets so that the brackets can be bolted to the plate. A diamond wire of 0.32 mm diameter was used to cut a 0.125 inch long groove starting at one hole of the sample in the direction parallel to the plate’s width. A 50 μm thick polyamide film (DuPont Kapton HN) was bonded next to the groove on one side of the sample using superglue. An antenna sensor (66 μm thick, 12.75 mm wide and 14 mm long, with a feed strip of 1.8 mm wide) was then made from a 0.5 inch wide copper tape (3M 1181). The patch was bonded to the plate at a distance of 0.1 inch from the groove tip and was oriented with its length dimension perpendicular to the groove, as shown in Figure 4. In order to connect the antenna sensor to a Vector Network Analyzer (VNA), an SMA connector was bonded to an aluminum spacer with its pin facing down, pressing on the feed line of the antenna sensor. The spacer was bonded to the sample plate with a fatigue-rated adhesive (Vishay M-Bond AE-15) and was allowed to cure at 80 degrees Celsius for four hours. The SMA connector was connected to the sensor’s feed strip with conductive epoxy. Since the patch was covered during the test, the exact location of the patch was marked on the opposite side of the sample. A grid was drawn using 2 mm increment markings so that the actual crack growth can be monitored visually using a CCD camera. A Kapton film was also bonded to one of the brackets so that a shielded antenna sensor is created when the bracket is mounted on the sample. The final step of the antenna fabrication process involves pre-compressing the antenna sensor with a 1250 lb force using the test frame so that excess superglue is removed and the antenna sensor is pre-conditioned to achieve a more consistent performance. Groove Antenna sensor SMA connector Spacer

Figure 4. Antenna sensor mounted on fatigue sample.

3. Experiment Set-up and Procedure

The experiment setup for fatigue testing the shield antenna sensor is shown in Figure 5. Both of the holding brackets were bolted to the plate using 3/8 inch UNC

J. Erdmann and H. Huang / Microwave Antenna Sensors for Fatigue Crack Monitoring

461

bolts, washers, and nuts. After securing the entire fixture in the MTS hydraulic clamps, the fixture was subjected to a static tension load of 100 lbs to ensure that all pieces were aligned properly before the bolts were tightened. The bolts were tightened using an analog torque wrench to control the applied torque at 75 in-lb. The compressive force F due to the bolt tightening can be approximated as

F 6 T / 0.21d  .

(4)

where F is the compressive force, T is the torque, and d is the major diameter of the bolt. Assuming the bolt is well-lubricated, the compressive force is calculated to be 952 lbs for a 75 in-lb torque. The actual force value is most likely lower since the bolts were not lubricated. In addition, the torque wrench reading may have an error of up to ±30% [10]. The resonant frequency of the antenna sensor was first measured using the VNA (Rohde & Schwarz ZVA24) at low static tensile loads of 100, 200, and 300 lb. This is to ensure that no major shifts in frequency were observed. A shift in frequency would have indicated that the antenna sensor was not set up properly. The fatigue sample was then subjected to cyclic loading for pre-cracking (5 Hz loading frequency, Pmax = 1200 lbs, and R = 0.3). Because of the single lap-joint configuration, the fatigue sample was subjected to a combined tension and bending load during the fatigue loading. The VNA was left attached to the antenna sensor for the duration of the test. A camera was placed near the back side of the plate and focused on the grid to monitor the crack growth during the test. A fiber optic light was used to illuminate the grid area. After approximately 55,000 cycles, no crack was visible on the grid, so the Pmax value was increased to 2000 lbs. When the crack began to propagate, VNA measurements were taken when the crack tip reached at and between each grid reference mark. The VNA took 1000 data points per 1 GHz span, which gives a frequency resolution of 1 MHz. When the crack Holding bracket

Fatigue sample SMA cable

Load frame Figure 5. Experiment setup for fatigue testing.

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J. Erdmann and H. Huang / Microwave Antenna Sensors for Fatigue Crack Monitoring

tip reached a measurement point, the fatigue loading was stopped and the sample was placed under static tension loads ranging from 700 lbs to 1900 lbs with 200 lb increments. VNA readings were obtained at each increasing tension increment. After all measurements were taken, the fatigue loading cycle was resumed until the crack reached the next measurement point. When the crack propagated to the edge of the measurement grid, the test was stopped and the fatigue sample was inspected. After inspection, the sample was placed back into the MTS tester and pulled apart so that the internal crack features could be observed.

4. Results and Discussions

We first evaluated the effect of the top plate on the resonant frequency of a regular antenna sensor, i.e. without the superstrate and the top ground plane. As shown in Figure 6, the addition of a top ground plane shifted the resonant frequency by about 6% but did not change the characteristics of the S11 curve drastically. It took approximately 72,000 cycles plus the initial 55,000 pre-cracking cycles for the crack to propagate through the grid that marks the patch location. During the fatigue experiment, the crack did not grow perfectly perpendicular to the patch length as desired; instead, it grew at an angle of approximately 36 degrees at the beginning and slowly turned to be parallel to the width direction of the antenna patch, as shown in Figure 7a. This occurred because the groove cut by the diamond wire was not smooth, which caused the crack to start in a direction not parallel with the patch width. The compression force exerted by the tightened bolt may have altered the crack growth direction as well [11]. After the crack reached the far edge of the grid, the fixture was disassembled and the antenna patch was inspected. We discovered that the crack front and the crack surface was not perpendicular to the plate surface, i.e. the crack path on the sensor side was different from the crack path on the grid side. In order to compare the crack locations on both surfaces of the plate, a grid was marked on the patch surface at the exact location as the grid drawn on the other side, as shown in Figure 7b. When the crack had reached the edge of the antenna patch on the sensor side of the plate, the crack was at the 8 mm mark on the grid side. Breaking the plate and inspecting the crack surface verified that the crack was growing further ahead on the patch side and slanted toward the patch edge, as shown in Figure 7(c). The patch did not suffer any visible damage while undergoing the fatigue cycling, indicating that it can withstand a combine stress loading over multiple fatigue cycles.

Return Loss (dB)

0

-5

-10

Uncovered Covered

6

7

Frequency (GHz)

8

Figure 6. Effect of top plate on antenna resonant frequency.

J. Erdmann and H. Huang / Microwave Antenna Sensors for Fatigue Crack Monitoring

Fracture

Fatigue crack

463

Precrack

(a)

Fatigue crack

(b)

(c)

Figure 7. Images of fatigue crack; (a) crack on the back side of the sample. (b) crack on the sensor side of the sample. (c) fatigue and fracture surface.

The S11 curves of the antenna sensor while the test fixture was statically loaded at 1700 lbs were analyzed at different crack lengths. The shifts of the S11 curves with the crack growth are shown in Figure 8(a). The S11 curves show a shift in both f01 and f10 frequencies, indicating that the crack was not perfectly perpendicular to one dimension of the antenna patch. Otherwise, the crack would have only affected either the f01 or the f10 frequency. Therefore, the frequency shift of both resonant frequency peaks provides an indication on the crack growth direction. The shifts of the f01 and f10 frequency with the crack length are plotted in Figure 8(b). The crack lengths were measured based on the digital images of the crack on the grid side of the sample. The actual crack length on the sensor side was slightly different since the crack front was not perpendicular to the crack growth direction and the crack surface was slanted. As shown in Figure 8(b), the f10 frequency shifts linearly with the crack growth until the crack length reached 6 mm. The crack sensitivity of the antenna sensor was estimated to be 28.6 MHz frequency shift for every 1 mm crack growth. As the crack propagated beyond the edge of the antenna patch, at approximately 6 mm, the frequency shifts were not as significant, decreasing to 2 MHz between 6 and 7 mm. This is because the crack was outside of the antenna patch, it had very little influences on the current flow of the TM10 mode. At approximately 8 mm, the frequency spikes to a slightly higher value. This spike may be an indication of decreased crack opening due to the geometry of the crack growth. After 8 mm, the f10 frequency starts to decrease again. The crack sensitivity for the last three data points on Figure 8(b) is 18.5 MHz/mm. The decrease in the f10 frequency for crack length longer than 8 mm is likely contributed by the stretching of the antenna patch due to crack opening. As the crack length increases, the crack opening at the location of the antenna patch increases. As a result, the antenna patch elongates with the crack opening, causing the f10 frequency to decrease.

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J. Erdmann and H. Huang / Microwave Antenna Sensors for Fatigue Crack Monitoring

Return Loss (dB)

-2 -4

2 3 4 5 6 7

-6

8 9 10 End

-8 6

6.5

7

7.5

8

Frequency (GHz)

7.82

8.5

7.2

y = 0.0286x + 7.8554 R² = 0.9603

7.77

Frequency (GHz)

Frequency (GHz)

(a)

7.72 7.67 7.62 0

2

4

6

8

Crack Growth (mm)

7 y = 0.047x + 6.69 R² = 0.9946

6.8 6.6 6.4

10

0

2

4

6

8

Crack Growth (mm)

(b)

10

(c)

Figure 8. Shift of (a) S11 curve; (b) f10 frequency; (c) f01 frequency with crack growth at a crack opening load of 1700 lbs.

Sensitivity (MHz/mm)

The shift of the f01 frequency with the crack growth, however, was much more complicated, as shown in Figure 8(c). It decreased at a crack sensitivity of 47 MHz/mm for the first 4 mm of crack growth. A large upward shift in the f01 frequency as the crack propagated to 5 mm was observed. This shift is caused by the high current density region at the edge of the antenna patch. As the crack approaches the width edge of the sensor, it enters a high current density region of the TM01 radiation mode, which causes the upward shift in the f01 frequency [8]. The sudden frequency drop occurs when the crack passes beyond this region. The crack sensitivity of the f10 frequency at different loading levels is shown in 35 30 25 20 15 10 5 0 700

900

1100

1300

1500

1700

Load (lbs) Figure 9. Sensitivity change of f10 frequency with increased crack opening.

J. Erdmann and H. Huang / Microwave Antenna Sensors for Fatigue Crack Monitoring

465

Figure 9. The sensitivities are around 25 MHz/mm for loads higher than 900 lbs. This indicates that the crack sensitivity of the antenna sensor is not sensitive to the external loading as long as the load is sufficiently large to open the crack fully. For a smaller load, e.g. 700 lbs, the crack may be partially closed, resulting in a substantially lower sensitivity. The capability to monitor crack opening is another advantage of the antenna sensor since crack closure plays an important role in determining the remaining service life of a cracked component [8].

5. Conclusions

We have demonstrated that a shielded microstrip patch antenna is able to determine the location, size, and orientation of a crack under a lap joint. The patch antenna was able to withstand the combined stress environment over more than 100,000 cycles.

Acknowledgement

This project is partially supported by the National Science Foundation CAREER award CMMI-0846074. The support and encouragement of the program manager, Dr. Shih-Chi Liu, is greatly appreciated.

References [1] NTSB, 1989, Aircraft Accident Report, AAR-89-03, http://www.ntsb.gov/publictn/1989/AAR8903.htm. [2] J.B. Ihn, and F.K. Chang Multi-crack Growth Monitoring at Riveted Lap-joints Using Piezoelectric Patches, Smart Nondestructive Evaluation for Health Monitoring of Structural and Biological Systems, 4702 (2002), 29-40. [3] M. Lin, X. Qing, A. Kumar, and S.J. Beard, Smart Layer and Smart Suitcase for Structural Health Monitoring Applications, Smart Structures and Materials, 4332 (2001), 98-106. [4] B.C. Lee and W.J. Staszewski Modelling of Lamb Waves for Damage in Metallic Structures: Part II. Wave Interactions with Damage, Smart Materials and Structures, 12 (2003), 815-824. [5] G. Grandhi, F. Nkrumah, M.J. Sundaresan, J. Kemerling, and D. Thomas, Monitoring Fatigue Crack Growth in 7075 T6 Aluminum Using Continuous Sensor, Smart Materials and Structures, 5764 (2005), 595-602. [6] Diraison, L. Y., Joubert, P., and Placko, D., 2009, “Characterization of Subsurface Defects in Aeronautical Riveted Lap-joints Using Multi-frequency Eddy Current Imaging,” NDT&E International, 42, pp. 133-140. [7] N. Goldfine, V. Zilberstein, A. Washabaugh, D. Schlicker, I. Shay, and D. Grundy, Eddy Current Sensor Networks for Aircraft Fatigue Monitoring, Aerospace Health Monitoring, 61 (2003), 1-13. [8] I. Mohammad and H. Huang, Monitoring Fatigue Crack Growth and Opening Using Antenna Sensors, Smart Materials and Structures, 19 (2010), 1-8. [9] C.A. Balanis, Antenna Theory: Analysis and Design, John Wiley & Sons, New Jersey, C. A., 2005, 816819. [10] R. L. Norton, Machine Design: An Integrated Approach, Pearson Prentice Hall, New Jersey, 2006, 854855. [11] K. Shankar and R. Dhamari, Fatigue Behavior of Aluminum Alloy 7075 Bolted Joints Treated with Oily Film Corrosion Compounds, Materials and Design, 23 (2002), 211-212.

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467

Subject Index 3MA 322 acoustoelastic effect 164 active thermography 402 air gap estimation 288 AMR 211 ancillary yoke pole 275 antenna sensor 456 arc simulation 425 asymptotic boundary conditions 173 Barkhausen noise 225 behavioral inverse model 288 BEM 173 BEMLAB 173 Bjőrk-Shiley convexo concave prosthetic heart valve 296 bolthole cracks 36 boundary element method 96, 173 carbon fiber reinforced plastics 447 CFRP 362 comb actuators 173 comb capacitors 173 combustion chamber 211 commutation phenomenon 432, 439 complex permittivity 410 computed tomography 30 concealed frescos detection 402 condition monitoring 267 conical Swiss roll 362 control magnetic methods 339 corrosion protection 417 Cr depletion 355 crack 134, 410 crack modelling 96 cracks recognition 61 creep damage 347 Cr-Mo-V steel 347 CUDA 117 decision analysis 71 defects detection algorithms 417 depth estimation 53 detection of small defects 22 dielectric 389 diet pulses 183

differential exciting mode 203 discrete complex image method 96 dual layer 275 duplex stainless steel 311 dyadic Green functions 134 dynamical hysteresis loop 347 ECT 211 ECT signal inversions 103 eddy current non destructive testing 149 eddy current testing 22, 71, 96, 134, 241, 249, 282 eddy current transmission mode 330 eddy currents 13, 53, 103, 141, 192, 288, 296, 311 eddy currents inspection 183 eddy-current NDE 36 electric potential difference 3 electromagnetic nondestructive evaluation 362, 447 electromagnetic testing 44 electromagnetic wave 111 electromagnetic-acoustic transducer 125 EMAT 164, 225, 322 excitation and sensing system 233 fast multipole method 79 fatigue crack monitoring 456 FEM 111 ferromagnetism 134 FG sensor 203 film thickness 330 finite element method (FEM) 44, 432, 439 finite element model 256 flow-accelerated corrosion 267 forward analysis 3 Galerkin’s method 87 giant magneto-impedance sensor 149 giant magneto-resistance sensor 149 giant magnetoresistive sensor 13 GMR 217 GMR sensor 256

468

GPGPU 117 GPR 381 Green’s dyad formalism 149 half-analytical method 183 Hall sensor array 425 high order basis functions 87 Hilbert transformation 225 image processing 302 image reconstruction 225, 447 imperialist competitive algorithm 192 Inconel 355 integral formulation 134 inverse problem 192 IQI 302 lap-joint 456 local wall thinning 203, 241 long range ultrasonic technology 125 low carbon steel 347 magnetic adaptive testing 371 magnetic flux leakage (MFL) 217, 256, 275 magnetic hysteresis curve 355 magnetic hysteresis measurements 371 magneto-mechanical effect 339 magnetostatic regime 87 material defect 233 measurement of arc movement 425 measuring system 249 MEMS 173 metamaterials 362 metamodel-based inversion 71 method of moments 79 micro-electro-mechanical systems 173 microwave frequency 410 microwave heating 402 microwave interferometry 389 monotonicity 103 Monte Carlo methods 355 multi-defects analysis 183 multi-frequency approach 288 multilayered aeronautical structure 288 multi-layered structure 13 multiple cracks 117 multi-threading 173 MUSIC-type algorithm 22 NDT 217, 389, 410

NDT by magnetic flux leakage 87 neutron embrittlement 322 nondestructive test 3, 267 non-destructive evaluation 53, 103, 125, 192, 288, 347, 355 non-destructive inspection 296, 302 non-iterative imaging algorithms 103 non-iterative inversion 22 nonlinear media 87 numerical modeling 125 object recognition 157 objectivity 173 open source 173 outlet strut fractures 296 pancake coil 241 partially conductive cracks 53 particle swarm optimization 71 pipe wall thinning 3 piping detection 111 plastic deformation 347 polarization 164 polynomial chaos 141 pressure vessel 322 probabilistic collocation method 141 pulsed ECT 203 pulsed eddy currents 233 radiogram 302 radiography 30, 157 reconstruction 217 reinforcing plate 275 residual magnetic field 339 residual stress 164 sensitivity analysis 61 sensor tilt 13 shape recognition 381 sigma phase 311 signal and image processing 381 signal processing 267 singularity 79 Sommerfeld integrals 96 sparking voltage 439 spherical defects 44 state function 432, 439 stress 339 stress corrosion cracks 282 structural health monitoring 456 surface integral crack model 117 surface integral equations 79 sweep frequency 296

469

switch gear thin film technology thin-skin theory THz imaging time domain inspection time-domain field analysis titanium alloys inspections track rope

425 330 36 417 417 61 249 256

ultrasonic NDE 164 ultrasonic waves 125 uncertainty 53 universal motor 432, 439 UXO 381 wall thinning 111, 275 waveguide reflection method 410

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471

Author Index Akiyama, Y. Aldrin, J.C. Alman, M. Altpeter, I. Andreescu, A. Anheuser, M. Ara, K. Areiza, M.C.L. Baniukiewicz, P. Barsanescu, P.D. Bisiaux, B. Blodgett, M.P. Blome, M. Bonnet, M. Bouali, F. Bruma, A. Brykalski, A. Burke, S.K. Calvano, F. Capova, K. Caryk, M. Casperson, R. Chady, T. Chlewicki, W. Cung, T.L. Decitre, J.-M. Demachi, K. Dobmann, G. Douvenot, R. Erdmann, J. Faktorová, D. Feliachi, M. Fnaiech, E.A. Gawrylczyk, K.M. Gratkowski, S. Grimberg, R. Gyimóthy, S. Hamel, A. Hasizume, H. He, D. Henriksson, T. Heuer, H.

432, 439 141 53 322 381 425 275 311 30, 157, 302 447 87 141 217 79 183 362 30 36 103 233, 296 302 44 v, 30, 249, 282, 302, 417 30 288 134 164 322 71 456 410 183, 192 87 61 v, 125 362, 381, 447 117 192 111 211 22 330

Hillmann, S. Honda, S. Huang, H. Hübschen, G. Iftimie, N. Janousek, L. Jayakumar, T. Jia, J. Joubert, P.Y. Kamada, Y. Kikuchi, H. Kiss, I. Klein, M. Knopp, J.S. Kobayashi, S. Kojima, F. Kopp, M. Kosaka, D. Kosse, S. Kowalczyk, J. Kreutzbruck, M. Lambert, M. Leitoiu, S. Lesiecki, P. Lesselier, D. Lim, T. Little, J. Łopato, P. Mahadevan, S. Marchand, C. Michniakova, M. Mohellebi, H. Moriya, S. Napierała, L. Nawos-Wysocki, L. Neubauer, A. Nishimura, Y. Nittono, O. Niwa, Y. Ohtani, T. Okazaki, H. Okita, K. Pávó, J.

330 3 456 322 362, 381 53, 233, 296 256 211 288 275, 347 275, 347 117 330 141 275, 347 267 322 267 425 249, 282 44, 217 22, 71, 134 381 402 22, 71 79 389 302, 417 256 87 233 183, 192 211 302 249 217 225 355 432, 439 347 347 211 117

472

Pei, C. Pelkner, M. Pichenot, G. Pietrusewicz, T. Prémel, D. Psuj, G. Raj, B. Rao, B.P.C. Rebello, J.M.A. Reboud, C. Reimund, V. Roskosz, M. Rubinacci, G. Sacramento, R. Sakai, Y. Salavastru, D.P. Santos de Assis, K. Sasamoto, A. Savin, A. Schmidt, H.-P. Schmidt, K. Serghiac, B. Shimizu, I. Shiwa, M. Sikora, J. Sikora, R. Singh, W.S. Smetana, M. Spychalski, I. Steigmann, R. Strapacova, T. Suzuki, K.

164 44, 217 79, 149 302 87, 149 249, 282, 302 256 256 311, 417 134 44, 217 339 103 311 111 447 311 225 362, 381, 447 425 389 447 275 211 173 157, 302 256 53, 233, 296 249 362, 447 296 355

Suzuki, T. 225 Szymanik, B. 402 Takagi, T. v, 203, 241, 355, 371 Takara, T. 355 Takase, T. 355 Takatsubo, J. 211 Tamburrino, A. 103 Theodoulidis, T. 96 Thomas, H.-M. 44, 217 Tomáš, I. 371 Tschuncky, R. 322 Tsukidate, S. 347 Uchimoto, T. 203, 241, 355, 371 Udpa, L. 13 Udpa, S.S. v, 13 Ueda, S. 371 Uetake, I. 211 Umetani, K. 267 Ventre, S. 103 Vértesy, G. 371 Vértesy, Z. 371 Vourc’h, E. 288 Wieleba, P. 173 Xie, S. 203 Yamaguchi, K. 355 Yamamoto, T. 203, 241 Yamawaki, H. 211 Yang, G. 13 Yusa, N. 111 Zeng, Z. 13 Ziolkowski, M. 125 Zorni, C. 134

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